Quelle NumericalSgps.bib Sprache: Latech

@incollection {JMDA,
    AUTHOR = {Delgado, M. and Garc\'{\i}a-S\'anchez, P. A. and Morais, J.},
     TITLE = {On the {GAP} package numericalsgps},
BOOKTITLE = {Fifth {C}onference on {D}iscrete {M}athematics and {C}omputer
              {S}cience ({S}panish)},
    SERIES = {Ciencias (Valladolid)},
    VOLUME = {23},
     PAGES = {271--278},
PUBLISHER = {Univ. Valladolid},
   ADDRESS = {Secr. Publ. Intercamb. Ed., Valladolid},
      YEAR = {2006},
   MRCLASS = {20-04},
  MRNUMBER = {2325970},
}

@article {MR1283022,
     AUTHOR = "Contejean, E. and Devie, H.",
      TITLE = "An efficient incremental algorithm for solving systems of
               linear {D}iophantine equations",
    JOURNAL = "Inform. and Comput.",
   FJOURNAL = "Information and Computation",
     VOLUME = "113",
       YEAR = "1994",
     NUMBER = "1",
      PAGES = "143--172",
       ISSN = "0890-5401",
    MRCLASS = "11Y50 (11D04 68Q20)",
   MRNUMBER = "MR1283022 (96a:11151)",
MRREVIEWER = "B\'ela Vizv\'ari"
}

@Article{HS04,
author= "Herzinger, K. and Sanford, R.",
title= "Minimal Generating Sets for Relative Ideals in Numerical Semigroups of Multiplicity Eight",
journal= "Communications in Algebra",
volume= "32",
number = "12",
year= "2004",
pages= "4713-4731"
}

@Article{R96,
author= "Rosales, J. C.",
title= "On numerical semigroups",
journal= "Semigroup Forum",
volume= "52",
year= "1996",
pages= "307-318"
}

@Book{RGS99,
author= "Rosales, J. C. and Garc\'{\i}a-S\'anchez, P. A.",
title= "Finitely generated commutative monoids",
year= "1999",
publisher= "Nova Science Publishers",
address= "New York"
}

@Article{RGGU03,
author= "Rosales, J. C. and Garc\'{\i}a-S\'anchez P. A. and Garc\'{\i}a-Garc\'{\i}a, J. I. and Urbano-Blanco, J. M.",
title= "Proportionally modular Diophantine inequalities",
journal= "J. Number Theory",
volume= "103",
year= "2003",
pages= "281-294"
}

@Article{RGGJ03,
author= "Rosales, J. C. and Garc\'{\i}a-S\'anchez, P. A. and Garc\'{\i}a-Garc\'{\i}a, J. I. and Jim\'enez-Madrid, J. A.",
title= "The oversemigroups of a numerical semigroup",
journal= "Semigroup Forum",
volume= "67",
year= "2003",
pages= "145-158"
}

@Article{Ros96,
author= "Rosales, J. C.",
title= "An algorithmic method to compute a minimal relation for any numerical semigroup",
journal= "Internat. J. Algebra Comput.",
volume= "6",
year= "1996",
pages= "441-455"
}

@Article{RGS04,
author= "Rosales, J. C. and Garc\'{\i}a-S\'anchez, P. A.",
title= "Every positive integer is the Frobenius number
        of an irreducible numerical semigroup with at most four generators",
journal= "Ark. Mat.",
volume= "42",
year= "2004",
pages= "301-306"
}

@BOOK{BDF97,
  title = {Maximality properties in numerical semigroups and applications to
one-dimensional analytically irreducible local domains},
  publisher = {American Mathematical Society},
  year = {1997},
  author = {Barucci, V. and Dobbs, D. D. and Fontana, M.},
  number = {598},
  series = {Memoirs of the American Mathematical Society}
}

@Article {FGH87,
    AUTHOR = {Fr\"oberg, R. and Gottlieb, C. and H\"aggkvist R.},
     TITLE = {On numerical semigroups},
   JOURNAL = {Semigroup Forum},
  FJOURNAL = {Semigroup Forum},
    VOLUME = {35},
      YEAR = {1987},
    NUMBER = {1},
     PAGES = {63--83}
}

@Article {RB03,
    AUTHOR = {Rosales, J. C. and Branco, M. B.},
     TITLE = {Irreducible numerical semigroups},
   JOURNAL = {Pacific J. Math.},
  FJOURNAL = {Pacific Journal of Mathematics},
    VOLUME = {209},
      YEAR = {2003},
    NUMBER = {1},
     PAGES = {131--143}
}

@Article {RGGB04,
    AUTHOR = {Rosales, J. C. and Garc\'{\i}a-S\'anchez, P. A. and Garc\'{\i}a-Garc\'{\i}a, J. I. and Branco, M. B.},
     TITLE = {Arf numerical semigroups},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {276},
      YEAR = {2004},
     PAGES = {3--12}
}

@Article {RGGB03,
    AUTHOR = {Rosales, J. C. and Garc\'{\i}a-S\'anchez, P. A. and Garc\'{\i}a-Garc\'{\i}a, J. I. and Branco, M. B.},
     TITLE = {Numerical semigroups with maximal embedding dimension},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {2},
      YEAR = {2003},
     PAGES = {47--53}
}

@Article{Ros05,
   AUTHOR = {Bullejos, M. and Rosales, J. C.},
     TITLE = {Proportionally modular {D}iophantine inequalities and the
              {S}tern-{B}rocot tree},
   JOURNAL = {Math. Comp.},
  FJOURNAL = {Mathematics of Computation},
    VOLUME = {78},
      YEAR = {2009},
    NUMBER = {266},
     PAGES = {1211--1226},
      ISSN = {0025-5718},
     CODEN = {MCMPAF},
   MRCLASS = {20M14 (11D75)},
  MRNUMBER = {2476582 (2010d:20063)},
MRREVIEWER = {P. G. Trotter},
       DOI = {10.1090/S0025-5718-08-02173-X},
       URL = {https://doi.org/10.1090/S0025-5718-08-02173-X},
}

@Book{GHKb,
author= "Geroldinger, A. and Halter-Koch, F.",
title= "Non-unique Factorizations: Algebraic, Combinatorial and
Analytic Theory",
year= "2006",
publisher= "Chapman \& Hall/CRC"
}

@Article{CGLPR,
author= "Chapman, S. T. and Garc\'{\i}a-S\'anchez, P. A. and Llena, D. and Ponomarenko, V. and Rosales, J. C.",
title = {The catenary and tame degree in finitely generated commutative cancellative
monoids},
  journal = {Manuscripta Math.},
  year = {2006},
  volume = {120},
  pages = {253--264},
  number = {3}
}

@Article{CGL,
author= "Chapman, S. T. and Garc\'{\i}a-S\'anchez, P. A. and Llena D.",
title= "The catenary and tame degree of numerical semigroups",
  journal = {Forum Math.},
  year = {2007},
  pages = {1--13}
}

@Article{CHM06,
author= "Chapman, S. T. and Holden, M. T. and Moore, T. A.",
title= "Full elasticity in atomic monoids and integral domains",
journal= {Rocky Mountain J. Math.},
Volume = {36},
Number ={5},
year = 2006,
Pages = {1437--1455}
}

@Article{BF06,
author= {Barucci, V. and Fr\"oberg, R.},
title= "Associated graded rings of one-dimensional analytically
irreducible rings",
journal= "J. Algebra",
volume= "304",
year= "2006",
pages = "349--358"
}

@Article{E01,
author= "Elias, J.",
title= "On the deep structure of the blowing-up of curve singularities",
journal= "Math. Proc. Camb. Phil. Soc.",
volume= "131",
year= "2001",
pages= "227--240"
}

@Article{B06,
author= "Barucci, V.",
title= "Numerical semiroup algebras",
journal= "Multiplicative Ideal Theory in Commutative Algebra,
a tribute to the work of Robert Gilmer",
publisher= "Springer Science and Business Media",
year="2006"
}

@ARTICLE{VMic02,
  author = {Micale, V.},
  title = {On monomial semigroups},
  journal = {Communications in Algebra},
  year = {2002},
  volume = {30},
  pages = {4687 - 4698}
}
@ARTICLE{B-A08,
  author = {Bras-Amor\'os, M.},
  title = {Fibonacci-like behavior of the number of numerical semigroups of
a given genus},
  journal = {Semigroup Forum},
  year = {2008},
  volume = {76},
  pages = {379--384}
}

@article {BA-GS,
    AUTHOR = {Bras-Amor{\'o}s, Maria and Garc{\'{\i}}a-S{\'a}nchez, Pedro
              A.},
     TITLE = {Patterns on numerical semigroups},
   JOURNAL = {Linear Algebra Appl.},
  FJOURNAL = {Linear Algebra and its Applications},
    VOLUME = {414},
      YEAR = {2006},
    NUMBER = {2-3},
     PAGES = {652--669},
      ISSN = {0024-3795},
     CODEN = {LAAPAW},
   MRCLASS = {20M14},
  MRNUMBER = {2214415 (2007b:20129)},
MRREVIEWER = {Andrei Kelarev},
       DOI = {10.1016/j.laa.2005.11.007},
       URL = {https://doi.org/10.1016/j.laa.2005.11.007},
}

@Article{GS-O,
author= "Garc\'{\i}a-S\'anchez, P. A. and Ojeda, I.",
title= "Uniquely presented finitely generated commutative monoids",
journal= "Pacific J. Math.",
volume= "249",
year= "2010",
pages = "91--105"
}

@Article{B-GS-G,
author= "Blanco, V. and Garc\'{\i}a-S\'anchez, P. A. and Geroldinger, A",
title= "Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids",
journal= "Illinois J. Math.",
volume= "55",
year= "2011",
pages = "1385--1414"
}

@Article{DA-M-M,
author= "D'Anna, M. and Mezzasalma, M. and Micale V.",
title="On the Buchsbaumness of the associated graded ring of a one-dimensional local ring",
journal="Comm. Algebra",
volume="37",
year= "2009",
pages="1594--1603"
}

@article {DA-M-S,
    AUTHOR = {D'Anna, M. and Micale, V. and Sammartano, A.},
     TITLE = {On the associated graded ring of a semigroup ring},
   JOURNAL = {J. Commut. Algebra},
  FJOURNAL = {Journal of Commutative Algebra},
    VOLUME = {3},
      YEAR = {2011},
    NUMBER = {2},
     PAGES = {147--168},
      ISSN = {1939-0807},
   MRCLASS = {13A30 (13H10)},
  MRNUMBER = {2813470},
}

@Article {Br,
    AUTHOR = {Bryant, L.},
     TITLE = {Goto numbers of a numerical semigroup ring and the
              {G}orensteiness of associated graded rings},
   JOURNAL = {Comm. Algebra},
  FJOURNAL = {Communications in Algebra},
    VOLUME = {38},
      YEAR = {2010},
    NUMBER = {6},
     PAGES = {2092--2128},
      ISSN = {0092-7872},
     CODEN = {COALDM},
   MRCLASS = {20M25 (13A30 13C40 20M14)},
  MRNUMBER = {2675524},
MRREVIEWER = {Grigori I. {\v{Z}}itomirski{\u\i}},
       DOI = {10.1080/00927870903025993},
       URL = {https://doi.org/10.1080/00927870903025993},
}

@Article{BR13,
    AUTHOR = {Blanco, Victor and Rosales, Jos{\'e} Carlos},
     TITLE = {The tree of irreducible numerical semigroups with fixed
              {F}robenius number},
   JOURNAL = {Forum Math.},
  FJOURNAL = {Forum Mathematicum},
    VOLUME = {25},
      YEAR = {2013},
    NUMBER = {6},
     PAGES = {1249--1261},
      ISSN = {0933-7741},
   MRCLASS = {11D07 (05A18 13H10 20M14)},
  MRNUMBER = {3199729},
MRREVIEWER = {Raheleh Jafari},
       DOI = {10.1515/form.2011.151},
       URL = {https://doi.org/10.1515/form.2011.151},
}

@article {MR3169635,
    AUTHOR = {Rosales, J. C. and Garc{\'{\i}}a-S{\'a}nchez, P. A.},
     TITLE = {Constructing almost symmetric numerical semigroups from
              irreducible numerical semigroups},
   JOURNAL = {Comm. Algebra},
  FJOURNAL = {Communications in Algebra},
    VOLUME = {42},
      YEAR = {2014},
    NUMBER = {3},
     PAGES = {1362--1367},
      ISSN = {0092-7872},
   MRCLASS = {20M14 (20M25)},
  MRNUMBER = {3169635},
MRREVIEWER = {Attila Nagy},
       DOI = {10.1080/00927872.2012.740117},
       URL = {https://doi.org/10.1080/00927872.2012.740117},
}

@article {MR3354072,
    AUTHOR = {Spirito, Dario},
     TITLE = {Star operations on numerical semigroups},
   JOURNAL = {Comm. Algebra},
  FJOURNAL = {Communications in Algebra},
    VOLUME = {43},
      YEAR = {2015},
    NUMBER = {7},
     PAGES = {2943--2963},
      ISSN = {0092-7872},
   MRCLASS = {20M14 (13A99)},
  MRNUMBER = {3354072},
       DOI = {10.1080/00927872.2014.908201},
       URL = {https://doi.org/10.1080/00927872.2014.908201},
}

@Article{BF97,
author={Barucci, V. and Fr\"oberg, R.},
title={One-dimensional almost Gorenstein Rings},
journal={J. Algebra},
volume={188},
year={1997},
pages={418--442}
}

@article {BC77,
    AUTHOR = {Bertin, J. and Carbonne, P.},
     TITLE = {Semi-groupes d'entiers et application aux branches},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {49},
      YEAR = {1977},
    NUMBER = {1},
     PAGES = {81--95},
      ISSN = {0021-8693},
   MRCLASS = {14B05},
  MRNUMBER = {0568894 (58 \#27957)},
}

@article {KP95,
    AUTHOR = {Kirfel, Christoph and Pellikaan, Ruud},
     TITLE = {The minimum distance of codes in an array coming from
              telescopic semigroups},
      NOTE = {Special issue on algebraic geometry codes},
   JOURNAL = {IEEE Trans. Inform. Theory},
  FJOURNAL = {Institute of Electrical and Electronics Engineers.
              Transactions on Information Theory},
    VOLUME = {41},
      YEAR = {1995},
    NUMBER = {6, part 1},
     PAGES = {1720--1732},
      ISSN = {0018-9448},
     CODEN = {IETTAW},
   MRCLASS = {94B27 (94B35)},
  MRNUMBER = {1391031 (97e:94015)},
       DOI = {10.1109/18.476245},
       URL = {https://doi.org/10.1109/18.476245},
}

@article{AGS13,
author={Assi, A.  and  Garc\'{\i}a-S\'anchez, P. A.},
title={Constructing the set of complete intersection numerical semigroups with a given Frobenius number},
journal={Applicable Algebra in Engineering, Communication and Computing},
year={2013}
}

@article{AGS14,
author={Assi, A.  and  Garc\'{\i}a-S\'anchez, P. A.},
title={Algorithms for curves with one place at infinity},
journal= "Journal of Symbolic Computation",
volume= "74",
  pages= "475--492",
year= "2016"
}

@article{AGSM14,
author={Assi, A.  and  Garc\'{\i}a-S\'anchez, P. A. and V. Micale},
title={Bases of subalgebras of K[[x]] and K[x]},
journal= "Journal of Symbolic Computation",
volume= "79",
  pages= " 4--22",
year= "2017"
}

@book{Z86,
author={Zariski, O.},
title={Le probl\`eme des modules pour les courbes planes},
year={1986},
publisher={Hermann}
}

@BOOK{RGbook,
  title = {Numerical Semigroups},
  publisher = {Springer},
  year = {2009},
  author = {Rosales, J. C. and Garc\'{\i}a-S\'anchez, P. A.}
}

@article{DAMSwhen,
    AUTHOR = {D'Anna, M. and Micale, V. and Sammartano, A.},
     TITLE = {When the associated graded ring of a semigroup ring is
              complete intersection},
   JOURNAL = {J. Pure Appl. Algebra},
  FJOURNAL = {Journal of Pure and Applied Algebra},
    VOLUME = {217},
      YEAR = {2013},
    NUMBER = {6},
     PAGES = {1007--1017},
      ISSN = {0022-4049},
     CODEN = {JPAAA2},
   MRCLASS = {13A30 (13C40 14M10)},
  MRNUMBER = {3010100},
MRREVIEWER = {Zhongming Tang},
       DOI = {10.1016/j.jpaa.2012.09.024},
       URL = {https://doi.org/10.1016/j.jpaa.2012.09.024},
       }
@article{DAMSClasses,
    AUTHOR = {D'Anna, Marco and Micale, Vincenzo and Sammartano, Alessio},
     TITLE = {Classes of complete intersection numerical semigroups},
   JOURNAL = {Semigroup Forum},
  FJOURNAL = {Semigroup Forum},
    VOLUME = {88},
      YEAR = {2014},
    NUMBER = {2},
     PAGES = {453--467},
      ISSN = {0037-1912},
   MRCLASS = {20M14},
  MRNUMBER = {3189106},
MRREVIEWER = {M. A. Moreno-Fr{\'{\i}}as},
       DOI = {10.1007/s00233-013-9547-y},
       URL = {https://doi.org/10.1007/s00233-013-9547-y},
       }

@article{CJZ,
author={Cortadellas Ben\'{\i}tez, T. and  Jafari, R.  and Zarzuela Armengou, S.},
title={On teh Ap\'ery sets of monomial curves},
journal={Semigroup Forum},
year={2013},
volume={86},
pages={289--320},
doi={DOI 10.1007/s00233-012-9445-8}
}

@article{PH,
author={Philipp, A.},
title={A characterization of arithmetical invariants by the monoid of relations},
journal={Semigroup Forum},
volume={81},
year={2010},
pages={424--434}
}

@article {BH,
    AUTHOR = {Bryant, Lance and Hamblin, James},
     TITLE = {The maximal denumerant of a numerical semigroup},
   JOURNAL = {Semigroup Forum},
  FJOURNAL = {Semigroup Forum},
    VOLUME = {86},
      YEAR = {2013},
    NUMBER = {3},
     PAGES = {571--582},
      ISSN = {0037-1912},
     CODEN = {SMGFAN},
   MRCLASS = {20M14},
  MRNUMBER = {3053780},
       DOI = {10.1007/s00233-012-9448-5},
       URL = {https://doi.org/10.1007/s00233-012-9448-5},
}

@article {GSOSN,
    AUTHOR = {Garc{\'{\i}}a S{\'a}nchez, P. A. and Ojeda, I. and
              S{\'a}nchez-R.-Navarro, A.},
     TITLE = {Factorization invariants in half-factorial affine semigroups},
   JOURNAL = {Internat. J. Algebra Comput.},
  FJOURNAL = {International Journal of Algebra and Computation},
    VOLUME = {23},
      YEAR = {2013},
    NUMBER = {1},
     PAGES = {111--122},
      ISSN = {0218-1967},
   MRCLASS = {20M14 (20M13)},
  MRNUMBER = {3040805},
       DOI = {10.1142/S0218196713500033},
       URL = {https://doi.org/10.1142/S0218196713500033},
}

@book {CLOS,
    AUTHOR = {Cox, David and Little, John and O'Shea, Donal},
     TITLE = {Ideals, varieties, and algorithms},
    SERIES = {Undergraduate Texts in Mathematics},
   EDITION = {Third},
      NOTE = {An introduction to computational algebraic geometry and
              commutative algebra},
PUBLISHER = {Springer},
   ADDRESS = {New York},
      YEAR = {2007},
     PAGES = {xvi+551},
      ISBN = {978-0-387-35650-1; 0-387-35650-9},
   MRCLASS = {13P10 (13-01 14-01 14Qxx 68W30)},
  MRNUMBER = {2290010 (2007h:13036)},
       DOI = {10.1007/978-0-387-35651-8},
       URL = {https://doi.org/10.1007/978-0-387-35651-8},
}

@article {CHRA,
    AUTHOR = {Chappelon, Jonathan and Ram{\'{\i}}rez Alfons{\'{\i}}n, Jorge
              Luis},
     TITLE = {On the {M}\"obius function of the locally finite poset
              associated with a numerical semigroup},
   JOURNAL = {Semigroup Forum},
  FJOURNAL = {Semigroup Forum},
    VOLUME = {87},
      YEAR = {2013},
    NUMBER = {2},
     PAGES = {313--330},
      ISSN = {0037-1912},
   MRCLASS = {06F05 (05E05 06A06 20M14)},
  MRNUMBER = {3110597},
MRREVIEWER = {V{\'a}clav Koubek},
       DOI = {10.1007/s00233-012-9458-3},
       URL = {https://doi.org/10.1007/s00233-012-9458-3},
}

@incollection {BD-cyclotomic,
    AUTHOR = {Bradford, R. J. and Davenport, J. H.},
     TITLE = {Effective tests for cyclotomic polynomials},
BOOKTITLE = {Symbolic and algebraic computation ({R}ome, 1988)},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {358},
     PAGES = {244--251},
PUBLISHER = {Springer, Berlin},
      YEAR = {1989},
   MRCLASS = {11Y16 (11Y40)},
  MRNUMBER = {1034734 (90m:11201)},
MRREVIEWER = {Lajos R{\'o}nyai},
       DOI = {10.1007/3-540-51084-2_22},
       URL = {https://doi.org/10.1007/3-540-51084-2_22},
}

@Article{M,
    AUTHOR = {Moree, Pieter},
     TITLE = {Numerical semigroups, cyclotomic polynomials, and {B}ernoulli
              numbers},
   JOURNAL = {Amer. Math. Monthly},
  FJOURNAL = {American Mathematical Monthly},
    VOLUME = {121},
      YEAR = {2014},
    NUMBER = {10},
     PAGES = {890--902},
      ISSN = {0002-9890},
   MRCLASS = {11B68 (11C08)},
  MRNUMBER = {3295662},
       DOI = {10.4169/amer.math.monthly.121.10.890},
       URL = {https://doi.org/10.4169/amer.math.monthly.121.10.890},
       }

@article{SzW,
    AUTHOR = {Sz{\'e}kely, L. A. and Wormald, N. C.},
     TITLE = {Generating functions for the {F}robenius problem with {$2$}
              and {$3$} generators},
   JOURNAL = {Math. Chronicle},
  FJOURNAL = {Mathematical Chronicle},
    VOLUME = {15},
      YEAR = {1986},
     PAGES = {49--57},
      ISSN = {0581-1155},
     CODEN = {MTHCB3},
   MRCLASS = {05A15 (11D04 11P99)},
  MRNUMBER = {900339 (88i:05013)},
MRREVIEWER = {Volker Strehl},
}

@article{AG-GS,
    AUTHOR = {Aguil{\'o}-Gost, F. and Garc{\'{\i}}a-S{\'a}nchez, P. A.},
     TITLE = {Factoring in embedding dimension three numerical semigroups},
   JOURNAL = {Electron. J. Combin.},
  FJOURNAL = {Electronic Journal of Combinatorics},
    VOLUME = {17},
      YEAR = {2010},
    NUMBER = {1},
     PAGES = {Research Paper 138, 21},
      ISSN = {1077-8926},
   MRCLASS = {11D07 (05B45 05C90 11D45)},
  MRNUMBER = {2729387 (2011j:11050)},
MRREVIEWER = {Lajos Hajdu},
       DOI = {10.37236/410},
      URL = {https://doi.org/10.37236/410},
}

@article {B-P-ON,
    AUTHOR = {Barron, Thomas and O'Neill, Christopher and Pelayo, Roberto},
     TITLE = {On dynamic algorithms for factorization invariants in
              numerical monoids},
   JOURNAL = {Math. Comp.},
  FJOURNAL = {Mathematics of Computation},
    VOLUME = {86},
      YEAR = {2017},
    NUMBER = {307},
     PAGES = {2429--2447},
      ISSN = {0025-5718},
   MRCLASS = {20M14 (11Y11 68W40)},
  MRNUMBER = {3647965},
       DOI = {10.1090/mcom/3160},
       URL = {https://doi.org/10.1090/mcom/3160},
}

@article{GG-MF-VT,
AUTHOR = {Garc\'{\i}a-Garc\'{\i}a, J. I. and Moreno-Fr\'{\i}as, M. A. and Vigneron-Tenorio, A.},
TITLE = {Computation of Delta sets of numerical monoids},
JOURNAL = {Monatsh. Math. },
VOLUME = {178},
PAGES={457--472},
YEAR ={2015},
}

@misc{Normaliz,
AUTHOR={Bruns, W. and  Ichim, B. and  R\"omer, T.  and  S\"oger C.},
TITLE={Normaliz. Algorithms for rational cones and affine monoids},
YEAR={2014},
VERSION={2.12},
howpublished={\url{https://www.normaliz.uni-osnabrueck.de}},
}

@misc{Singular,
title = {{\sc Singular} {3-1-6} --- {A} computer algebra system for polynomial computations},
author = {Decker, Wolfram and Greuel, Gert-Martin and Pfister, Gerhard and Sch\"onemann, Hans},
year = {2012},
howpublished = {\url{https://www.singular.uni-kl.de}},
}

@misc{NmzInterface,
author={Gutsche, S and  Horn, M. and  S\"oger, C.},
title={NormalizInterface for GAP},
year={2014},
howpublished={\url{https://github.com/gap-packages/NormalizInterface}},
}

@misc{SingularInterface,
author={Barakat, M. and  Horn, M. and  Lübeck, F.  and Motsak, O. and  Neunhoeffer, M. and  Schoenemann H.},
title={SingularInterface for GAP},
year={2014},
howpublished={\url{https://github.com/gap-packages/SingularInterface.git}},
}

@misc{Singularpackage,
author={Costantini, M. and  de Graaf, W.},
year={2012},
title={GAP package singular; the GAP interface to Singular},
howpublished={\url{https://gap-system.org/Packages/singular.html}},
}

@article{R-GS-GG-B,
author = {Rosales,J. C. and Garc\'{\i}a-S\'anchez,P. A. and, Garc\'{\i}a-Garc\'{\i}a, J. I. and Branco, M. B.},
title = {SYSTEMS OF INEQUALITIES AND NUMERICAL SEMIGROUPS},
journal = {Journal of the London Mathematical Society},
volume = {65},
issue = {03},
month = {6},
year = {2002},
issn = {1469-7750},
pages = {611--623},
numpages = {13},
doi = {10.1112/S0024610701003052},
URL = {http://journals.cambridge.org/article_S0024610701003052},
}

@article{R-GS,
title = "Nonnegative elements of subgroups of $\mathbb{Z}^n$",
journal = "Linear Algebra and its Applications ",
volume = "270",
number = "1-3",
pages = "351- 357",
year = "1998",
note = "",
issn = "0024-3795",
doi = "https://doi.org/10.1016/S0024-3795(97)00309-1",
url = "http://www.sciencedirect.com/science/article/pii/S0024379597003091",
author = "J.C. Rosales and Pedro A. Garc\'{\i}a-S\'anchez",
abstract = "We give a method to compute all nonnegative integer solutions of a homogeneous system of linear equations. We use this method to provide an algorithm to compute all nonnegative integer solutions of homogeneous systems of equations having some of the equations in congruences. "
}

@article {MR1678508,
    AUTHOR = {Rosales, J. C. and Garc{\'{\i}}a-S{\'a}nchez, P. A.},
     TITLE = {On free affine semigroups},
   JOURNAL = {Semigroup Forum},
  FJOURNAL = {Semigroup Forum},
    VOLUME = {58},
      YEAR = {1999},
    NUMBER = {3},
     PAGES = {367--385},
      ISSN = {0037-1912},
     CODEN = {SMGFAN},
   MRCLASS = {13C40 (20M14)},
  MRNUMBER = {1678508 (2000j:13020)},
MRREVIEWER = {L{\^e} Tu{\^a}n Hoa},
       DOI = {10.1007/BF03325435},
       URL = {https://doi.org/10.1007/BF03325435},
}

@article {MR0269762,
    AUTHOR = {Herzog, J{\"u}rgen},
     TITLE = {Generators and relations of abelian semigroups and semigroup
              rings. },
   JOURNAL = {Manuscripta Math.},
  FJOURNAL = {Manuscripta Mathematica},
    VOLUME = {3},
      YEAR = {1970},
     PAGES = {175--193},
      ISSN = {0025-2611},
   MRCLASS = {20.93},
  MRNUMBER = {0269762 (42 \#4657)},
MRREVIEWER = {J. B. Kim},
}

@article {MR1394747,
    AUTHOR = {Eisenbud, David and Sturmfels, Bernd},
     TITLE = {Binomial ideals},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {84},
      YEAR = {1996},
    NUMBER = {1},
     PAGES = {1--45},
      ISSN = {0012-7094},
     CODEN = {DUMJAO},
   MRCLASS = {13P10 (13A30 14M25)},
  MRNUMBER = {1394747 (97d:13031)},
MRREVIEWER = {P. Schenzel},
       DOI = {10.1215/S0012-7094-96-08401-X},
       URL = {https://doi.org/10.1215/S0012-7094-96-08401-X},
}
@Misc{4ti2,
  author =   {4ti2 team},
  title =    {4ti2---A software package for algebraic, geometric and
              combinatorial problems on linear spaces},
  howpublished = {{A}vailable at www.4ti2.de}
}

@Misc{4ti2Interface,
  author =   {S. Gutsche},
  title =    {4ti2Interface, A link to 4ti2},
  howpublished = {\url{https://www.gap-system.org/Packages/4ti2interface.html}}
}

@misc{ GradedModules,
  author =           {Barakat,   M.   and   Gutsche,   S.   and  Jambor,  S.  and
                      Lange-Hegermann, M. and Lorenz, A. and Motsak, O.},
  title =            {{GradedModules},  A  homalg  based  package for the Abelian
                      category   of   finitely   presented  graded  modules  over
                      computable graded rings, {V}ersion 2014.09.17},
  month =            {Sep},
  year =             {2014},
  note =             {GAP package},
  howpublished =     {\href
                      {http://homalg.math.rwth-aachen.de/~barakat/homalg-project/Grjava.lang.NullPointerException
adedModules/}
                      {\texttt{http://homalg.math.rwth-aachen.de/}\discretionary
                      {}{}{}\texttt{\texttt{\symbol{126}}barakat/}\discretionary
                      {}{}{}\texttt{homalg-project/}\discretionary
                      {}{}{}\texttt{GradedModules/}}},
  keywords =         {modules;  graded modules; graduation; multi-graded modules;
                      Tate resolution},
  printedkey =       {BGJLLM14}
}

@article{DGSRP15,
   author = {Delgado, M. and Garc{\'{\i}}a-S{\'a}nchez, P.~A. and Robles-P{\'e}rez, A.~M.},
    title = {Numerical semigroups with a given set of pseudo-Frobenius numbers},
  journal = {LMS J. Comput. Math.},
keywords = {Mathematics - Commutative Algebra, Mathematics - Combinatorics, 11D07, 20M14, 20-04},
     year = {2016},
     volume= {19},
     pages={186--205}
}

@article{GSONW,
    AUTHOR = {Garc\'{\i}a-S\'{a}nchez, Pedro A. and O'Neill, Christopher and Webb,
              Gautam},
     TITLE = {The computation of factorization invariants for affine
              semigroups},
   JOURNAL = {J. Algebra Appl.},
  FJOURNAL = {Journal of Algebra and its Applications},
    VOLUME = {18},
      YEAR = {2019},
    NUMBER = {1},
     PAGES = {1950019, 21},
      ISSN = {0219-4988},
   MRCLASS = {20M13 (05A17 20M14)},
  MRNUMBER = {3910672},
MRREVIEWER = {Yan Hui Wang},
       DOI = {10.1142/S0219498819500191},
       URL = {https://doi.org/10.1142/S0219498819500191},
}

@article {E,
    AUTHOR = {Eliahou, Shalom},
     TITLE = {Wilf's conjecture and {M}acaulay's theorem},
   JOURNAL = {J. Eur. Math. Soc. (JEMS)},
  FJOURNAL = {Journal of the European Mathematical Society (JEMS)},
    VOLUME = {20},
      YEAR = {2018},
    NUMBER = {9},
     PAGES = {2105--2129},
      ISSN = {1435-9855},
   MRCLASS = {11B75 (05A10 05A20 13A02 20M14)},
  MRNUMBER = {3836842},
       DOI = {10.4171/JEMS/807},
       URL = {https://doi.org/10.4171/JEMS/807},
}

@article {Wilf,
    AUTHOR = {Wilf, Herbert S.},
     TITLE = {A circle-of-lights algorithm for the ``money-changing
              problem''},
   JOURNAL = {Amer. Math. Monthly},
  FJOURNAL = {The American Mathematical Monthly},
    VOLUME = {85},
      YEAR = {1978},
    NUMBER = {7},
     PAGES = {562--565},
      ISSN = {0002-9890},
   MRCLASS = {10A30 (05A17 68A10)},
  MRNUMBER = {0556658 (58 \#27728)},
MRREVIEWER = {Dennis White},
}

@article {Stokes,
    AUTHOR = {Stokes, Klara},
     TITLE = {Patterns of ideals of numerical semigroups},
   JOURNAL = {Semigroup Forum},
  FJOURNAL = {Semigroup Forum},
    VOLUME = {93},
      YEAR = {2016},
    NUMBER = {1},
     PAGES = {180--200},
      ISSN = {0037-1912},
   MRCLASS = {20M14 (11D07 20M12)},
  MRNUMBER = {3528435},
MRREVIEWER = {Andreas Reinhart},
       DOI = {10.1007/s00233-015-9741-1},
       URL = {https://doi.org/10.1007/s00233-015-9741-1},
}

@article {K-W,
    AUTHOR = {Kunz, E. and Waldi, R.},
     TITLE = {Geometrical illustration of numerical semigroups and of some
              of their invariants},
   JOURNAL = {Semigroup Forum},
  FJOURNAL = {Semigroup Forum},
    VOLUME = {89},
      YEAR = {2014},
    NUMBER = {3},
     PAGES = {664--691},
      ISSN = {0037-1912},
   MRCLASS = {20M14},
  MRNUMBER = {3274840},
MRREVIEWER = {Kurt D. Herzinger},
       DOI = {10.1007/s00233-014-9599-7},
       URL = {https://doi.org/10.1007/s00233-014-9599-7},
}

@article {DGSM,
    AUTHOR = {D'Anna, Marco and Garc\'{\i}a-S\'{a}nchez, Pedro A. and Micale,
              Vincenzo and Tozzo, Laura},
     TITLE = {Good subsemigroups of {$\Bbb N^n$}},
   JOURNAL = {Internat. J. Algebra Comput.},
  FJOURNAL = {International Journal of Algebra and Computation},
    VOLUME = {28},
      YEAR = {2018},
    NUMBER = {2},
     PAGES = {179--206},
      ISSN = {0218-1967},
   MRCLASS = {20M14},
  MRNUMBER = {3786416},
       DOI = {10.1142/S0218196718500091},
       URL = {https://doi.org/10.1142/S0218196718500091},
}

@article {MC-O-T,
    AUTHOR = {M{\'a}rquez-Campos, Guadalupe and Ojeda, Ignacio and Tornero,
              Jos{\'e} M.},
     TITLE = {On the computation of the {A}p\'ery set of numerical monoids
              and affine semigroups},
   JOURNAL = {Semigroup Forum},
  FJOURNAL = {Semigroup Forum},
    VOLUME = {91},
      YEAR = {2015},
    NUMBER = {1},
     PAGES = {139--158},
      ISSN = {0037-1912},
   MRCLASS = {20M14},
  MRNUMBER = {3369384},
MRREVIEWER = {Andreas Reinhart},
       DOI = {10.1007/s00233-014-9631-y},
       URL = {https://doi.org/10.1007/s00233-014-9631-y},
}

@article {Roune,
    AUTHOR = {Roune, Bjarke Hammersholt},
     TITLE = {Solving thousand-digit {F}robenius problems using {G}r\"obner
              bases},
   JOURNAL = {J. Symbolic Comput.},
  FJOURNAL = {Journal of Symbolic Computation},
    VOLUME = {43},
      YEAR = {2008},
    NUMBER = {1},
     PAGES = {1--7},
      ISSN = {0747-7171},
   MRCLASS = {13P10 (13D40 68W30)},
  MRNUMBER = {2381966},
MRREVIEWER = {Giancarlo Rinaldo},
       DOI = {10.1016/j.jsc.2007.06.002},
       URL = {https://doi.org/10.1016/j.jsc.2007.06.002},
}

@article{Ugolini,
    AUTHOR = {Ugolini, Simone},
     TITLE = {On numerical semigroups closed with respect to the action of
              affine maps},
   JOURNAL = {Publ. Math. Debrecen},
  FJOURNAL = {Publicationes Mathematicae Debrecen},
    VOLUME = {90},
      YEAR = {2017},
    NUMBER = {1-2},
     PAGES = {149--167},
      ISSN = {0033-3883},
   MRCLASS = {11A05 (11D04 11D07 20M14)},
  MRNUMBER = {3611782},
MRREVIEWER = {Lajos Hajdu},
       DOI = {10.5486/PMD.2017.7500},
       URL = {https://doi.org/10.5486/PMD.2017.7500},
}

@article {MR3493240,
    AUTHOR = {Delgado, M. and Garc{\'{\i}}a-S{\'a}nchez, P. A.},
     TITLE = {{numericalsgps}, a {GAP} package for numerical
              semigroups},
   JOURNAL = {ACM Commun. Comput. Algebra},
  FJOURNAL = {ACM Communications in Computer Algebra},
    VOLUME = {50},
      YEAR = {2016},
    NUMBER = {1},
     PAGES = {12--24},
      ISSN = {1932-2232},
   MRCLASS = {20-04 (20M14 68W30)},
  MRNUMBER = {3493240},
}

@article {arf-frob-gen,
  AUTHOR={Garc{\'{\i}}a-S{\'a}nchez, P. A. and  Heredia, B. A. and Karakas, H. I. and Rosales, J. C.},
  TITLE = {Parametrizing Arf numerical semigroups},
  JOURNAL = {J. Algebra Appl.},
  VOLUME = {16},
  YEAR = {2017},
  PAGES = {1750209 (31 pages)}
}

@article {duplication,
    AUTHOR = {D'Anna, M. and Strazzanti, F.},
     TITLE = {The numerical duplication of a numerical semigroup},
   JOURNAL = {Semigroup Forum},
  FJOURNAL = {Semigroup Forum},
    VOLUME = {87},
      YEAR = {2013},
    NUMBER = {1},
     PAGES = {149--160},
      ISSN = {0037-1912},
   MRCLASS = {20M12 (06B10 13A15 13A30 13F10 16D25)},
  MRNUMBER = {3079777},
MRREVIEWER = {Paula M. Machado Cruz Catarino},
       DOI = {10.1007/s00233-012-9451-x},
       URL = {https://doi.org/10.1007/s00233-012-9451-x},
}

@article {DA-G-H,
AUTHOR = {D'Anna, Marco and Guerrieri, Anna and Heinzer, William},
TITLE = {Invariants of ideals having principal reductions},
JOURNAL = {Comm. Algebra},
FJOURNAL = {Communications in Algebra},
VOLUME = {29},
YEAR = {2001},
NUMBER = {2},
PAGES = {889--906},
ISSN = {0092-7872},
MRCLASS = {13A15 (13C10)},
MRNUMBER = {1842007},
MRREVIEWER = {L. J. Ratliff, Jr.},
DOI = {10.1081/AGB-100001550},
URL = {https://doi.org/10.1081/AGB-100001550},
}

@article {Br-acute,
    AUTHOR = {Bras-Amor\'os, Maria},
     TITLE = {Acute semigroups, the order bound on the minimum distance, and
              the {F}eng-{R}ao improvements},
   JOURNAL = {IEEE Trans. Inform. Theory},
  FJOURNAL = {Institute of Electrical and Electronics Engineers.
              Transactions on Information Theory},
    VOLUME = {50},
      YEAR = {2004},
    NUMBER = {6},
     PAGES = {1282--1289},
      ISSN = {0018-9448},
   MRCLASS = {20M14 (94B27)},
  MRNUMBER = {2094884},
       DOI = {10.1109/TIT.2004.828104},
       URL = {https://doi.org/10.1109/TIT.2004.828104},
}

@incollection {bras-ns-codes,
    AUTHOR = {Bras-Amor\'{o}s, Maria},
     TITLE = {Numerical semigroups and codes},
BOOKTITLE = {Algebraic geometry modeling in information theory},
    SERIES = {Ser. Coding Theory Cryptol.},
    VOLUME = {8},
     PAGES = {167--218},
PUBLISHER = {World Sci. Publ., Hackensack, NJ},
      YEAR = {2013},
   MRCLASS = {94B27 (94B35)},
  MRNUMBER = {3288285},
MRREVIEWER = {John B. Little},
       DOI = {10.1142/9789814335768_0005},
       URL = {https://doi.org/10.1142/9789814335768_0005},
}

@article {A-A-GS,
    AUTHOR = {Abbas, A. and Assi, A. and Garc\'{\i}a-S\'{a}nchez, P. A.},
     TITLE = {Canonical bases of modules over one dimensional
              {$\bold{K}$}-algebras},
   JOURNAL = {Rev. R. Acad. Cienc. Exactas F\'{\i}s. Nat. Ser. A Mat. RACSAM},
  FJOURNAL = {Revista de la Real Academia de Ciencias Exactas, F\'{\i}sicas y
              Naturales. Serie A. Matematicas. RACSAM},
    VOLUME = {113},
      YEAR = {2019},
    NUMBER = {2},
     PAGES = {1121--1139},
      ISSN = {1578-7303},
   MRCLASS = {13F20 (05E15 14H50)},
  MRNUMBER = {3942387},
MRREVIEWER = {P. Schenzel},
       DOI = {10.1007/s13398-018-0538-4},
       URL = {https://doi.org/10.1007/s13398-018-0538-4},
}

@Article{DelgadoFarranGarcia-SanchezLlena2013MC,
  Title                    = {{On the generalized Feng-Rao numbers of numerical semigroups generated by intervals}},
  Author                   = {{Delgado}, M. and {Farr{\'a}n}, J.~I. and {Garc{\'{\i}}a-S{\'a}nchez}, P.~A. and {Llena}, D.},
  Journal                  = {Mathematics of Computation},
  Year                     = {2013},
  Number                   = {283},
  Pages                    = {1813--1836},
  Volume                   = {82},

  Adsnote                  = {Provided by the SAO/NASA Astrophysics Data System},
  Adsurl                   = {http://adsabs.harvard.edu/abs/2011arXiv1105.4833D},
  Archiveprefix            = {arXiv},
  Doi                      = {https://doi.org/10.1090/S0025-5718-2013-02673-7},
  Eprint                   = {1105.4833},
  Keywords                 = {Mathematics - Number Theory, 20M14, 11Y55, 11T71},
  Primaryclass             = {math.NT}
}

@article{BOR18,
    AUTHOR = {Branco, M. and  Ojeda, I. and Rosales, J. C.},
     TITLE = {Almost symmetric numerical semigroups with a given Frobenus number and type},
   JOURNAL = {preprint},
      YEAR = {2018},
}

@article{C-F-U,
author={Cisto, C. and Failla, G. and Utano R.},
title={On the generators of a generalized numerical semigroup},
journal={Analele Stiintifice ale Universitatii Ovidius Constanta},
year={2018},
}

@article {G-K,
AUTHOR = {Matsuoka, N. and Kumashiro, S.},
TITLE = {The generalized Gorenstein property and numerical semigroup rings obtained by gluing},
JOURNAL = {IMNS2010 - abstracts},
YEAR ={2017},
URL= {https://www.ugr.es/~imns2010/2018/Talks/NMatsuoka.pdf},
}

@ARTICLE{G-I-K-T,
   author = {{Goto}, S. and {Isobe}, R. and {Kumashiro}, S. and {Taniguchi}, N.
},
    title = "{Characterization of generalized Gorenstein rings}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1704.08901},
primaryClass = "math.AC",
keywords = {Mathematics - Commutative Algebra, 13H10, 13H15, 13A30},
     year = 2017,
    month = apr,
   adsurl = {http://adsabs.harvard.edu/abs/2017arXiv170408901G},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article {M00,
    AUTHOR = {Moree, P.},
     TITLE = {Approximation of singular series and automata},
      NOTE = {With an appendix by Gerhard Niklasch},
   JOURNAL = {Manuscripta Math.},
  FJOURNAL = {Manuscripta Mathematica},
    VOLUME = {101},
      YEAR = {2000},
    NUMBER = {3},
     PAGES = {385--399},
      ISSN = {0025-2611},
   MRCLASS = {11Y60 (11Y35)},
  MRNUMBER = {1751040},
MRREVIEWER = {M. Ram Murty},
       DOI = {10.1007/s002290050222},
       URL = {https://doi.org/10.1007/s002290050222},
}

@article {C-GS-M,
    AUTHOR = {Ciolan, Emil-Alexandru and Garc\'{i}a-S\'{a}nchez, Pedro A. and Moree,
              Pieter},
     TITLE = {Cyclotomic numerical semigroups},
   JOURNAL = {SIAM J. Discrete Math.},
  FJOURNAL = {SIAM Journal on Discrete Mathematics},
    VOLUME = {30},
      YEAR = {2016},
    NUMBER = {2},
     PAGES = {650--668},
      ISSN = {0895-4801},
   MRCLASS = {20M14 (11B68 11C08)},
  MRNUMBER = {3483156},
MRREVIEWER = {Alessio Moscariello},
       DOI = {10.1137/140989479},
       URL = {https://doi.org/10.1137/140989479},
}

@article{C-GS-HP-M,
    AUTHOR = {Ciolan, Emil-Alexandru and Garc\'{i}a-S\'{a}nchez, Pedro A. and Herrera-Poyatos, And\'es and Moree,
              Pieter},
     TITLE = {Cyclotomic exponent sequences of numerical semigroups},
   JOURNAL = {preprint},
      YEAR = {2019},
}

@incollection{M-Z,
    AUTHOR = {Maugeri, Nicola and Zito, Giuseppe},
     TITLE = {Embedding dimension of a good semigroup},
BOOKTITLE = {Numerical semigroups},
    SERIES = {Springer INdAM Ser.},
    VOLUME = {40},
     PAGES = {197--230},
PUBLISHER = {Springer, Cham},
      YEAR = {[2020] \copyright 2020},
   MRCLASS = {20M25 (13F20 14N05)},
  MRNUMBER = {4178261},
MRREVIEWER = {Huadong Su},
}

@article {B-DA-F-1,
    AUTHOR = {Barucci, V. and D'Anna, M. and Fr\"{o}berg, R.},
     TITLE = {The semigroup of values of a one-dimensional local ring with
              two minimal primes},
   JOURNAL = {Comm. Algebra},
  FJOURNAL = {Communications in Algebra},
    VOLUME = {28},
      YEAR = {2000},
    NUMBER = {8},
     PAGES = {3607--3633},
      ISSN = {0092-7872},
   MRCLASS = {13H10 (13A18 13B22 20M14)},
  MRNUMBER = {1767576},
MRREVIEWER = {Marco Fontana},
       DOI = {10.1080/00927870008827044},
       URL = {https://doi.org/10.1080/00927870008827044},
}

@article {B-DA-F-2,
    AUTHOR = {Barucci, V. and D'Anna, M. and Fr\"{o}berg, R.},
     TITLE = {Analytically unramified one-dimensional semilocal rings and
              their value semigroups},
   JOURNAL = {J. Pure Appl. Algebra},
  FJOURNAL = {Journal of Pure and Applied Algebra},
    VOLUME = {147},
      YEAR = {2000},
    NUMBER = {3},
     PAGES = {215--254},
      ISSN = {0022-4049},
   MRCLASS = {13H99 (13A18)},
  MRNUMBER = {1747441},
MRREVIEWER = {Ngo Viet Trung},
       DOI = {10.1016/S0022-4049(98)00160-1},
       URL = {https://doi.org/10.1016/S0022-4049(98)00160-1},
}

@article {DM,
    AUTHOR = {Delgado de la Mata, F\'{e}lix},
     TITLE = {Gorenstein curves and symmetry of the semigroup of values},
   JOURNAL = {Manuscripta Math.},
  FJOURNAL = {Manuscripta Mathematica},
    VOLUME = {61},
      YEAR = {1988},
    NUMBER = {3},
     PAGES = {285--296},
      ISSN = {0025-2611},
   MRCLASS = {14H20 (13H10 13J10)},
  MRNUMBER = {949819},
MRREVIEWER = {J\"{u}rgen Herzog},
       DOI = {10.1007/BF01258440},
       URL = {https://doi.org/10.1007/BF01258440},
}

@ARTICLE{BOR19,
    AUTHOR = {Branco, Manuel B. and Ojeda, Ignacio and Rosales, Jos\'{e} Carlos},
     TITLE = {The set of numerical semigroups of a given multiplicity and
              {F}robenius number},
   JOURNAL = {Port. Math.},
  FJOURNAL = {Portugaliae Mathematica. A Journal of the Portuguese
              Mathematical Society},
    VOLUME = {78},
      YEAR = {2021},
    NUMBER = {2},
     PAGES = {147--167},
      ISSN = {0032-5155},
   MRCLASS = {20M14 (11D07)},
  MRNUMBER = {4301804},
MRREVIEWER = {Michael Steward},
       DOI = {10.4171/pm/2064},
       URL = {https://doi.org/10.4171/pm/2064},
}

@book {fgcm,
    AUTHOR = {Rosales, J. C. and Garc\'{\i}a-S\'{a}nchez, P. A.},
     TITLE = {Finitely generated commutative monoids},
PUBLISHER = {Nova Science Publishers, Inc., Commack, NY},
      YEAR = {1999},
     PAGES = {xiv+185},
      ISBN = {1-56072-670-9},
   MRCLASS = {20M14},
  MRNUMBER = {1694173},
}

@book {nsapp,
    AUTHOR = {Assi, Abdallah and Garc\'{\i}a-S\'{a}nchez, Pedro A.},
     TITLE = {Numerical semigroups and applications},
    SERIES = {RSME Springer Series},
    VOLUME = {1},
PUBLISHER = {Springer, [Cham]},
      YEAR = {2016},
     PAGES = {xiv+106},
      ISBN = {978-3-319-41329-7; 978-3-319-41330-3},
   MRCLASS = {20M14 (14G50 14H50 68W30)},
  MRNUMBER = {3558713},
       DOI = {10.1007/978-3-319-41330-3},
       URL = {https://doi.org/10.1007/978-3-319-41330-3},
}

@book {nsapp2,
    AUTHOR = {Assi, Abdallah and D'Anna, Marco and Garc\'{\i}a-S\'{a}nchez, Pedro A.},
     TITLE = {Numerical semigroups and applications},
    SERIES = {RSME Springer Series},
    VOLUME = {3},
PUBLISHER = {Springer, [Cham]},
      YEAR = {2020},
     PAGES = {xiv+138},
      ISBN = {978-3-030-54942-8},
   MRCLASS = {20M14 (14G50 14H50 68W30)},
       DOI = {10.1007/978-3-030-54943-5},
       URL = {https://doi.org/10.1007/978-3-030-54943-5},
}

@article {R07,
    AUTHOR = {Rosales, J. C.},
     TITLE = {Subadditive periodic functions and numerical semigroups},
   JOURNAL = {J. Algebra Appl.},
  FJOURNAL = {Journal of Algebra and its Applications},
    VOLUME = {6},
      YEAR = {2007},
    NUMBER = {2},
     PAGES = {305--313},
      ISSN = {0219-4988},
   MRCLASS = {20M14},
  MRNUMBER = {2316425},
MRREVIEWER = {Attila Nagy},
       DOI = {10.1142/S0219498807002223},
       URL = {https://doi.org/10.1142/S0219498807002223},
}

@article {RGSGGJM,
    AUTHOR = {Rosales, J. C. and Garc\'{\i}a-S\'{a}nchez, P. A. and Garc\'{\i}a-Garc\'{\i}a, J.
              I. and Jim\'{e}nez Madrid, J. A.},
     TITLE = {Fundamental gaps in numerical semigroups},
   JOURNAL = {J. Pure Appl. Algebra},
  FJOURNAL = {Journal of Pure and Applied Algebra},
    VOLUME = {189},
      YEAR = {2004},
    NUMBER = {1-3},
     PAGES = {301--313},
      ISSN = {0022-4049},
   MRCLASS = {20M14},
  MRNUMBER = {2038577},
       DOI = {10.1016/j.jpaa.2003.10.024},
       URL = {https://doi.org/10.1016/j.jpaa.2003.10.024},
}

@article {RGSUB,
    AUTHOR = {Rosales, J. C. and Garc\'{\i}a-S\'{a}nchez, P. A. and Urbano-Blanco, J.
              M.},
     TITLE = {Modular {D}iophantine inequalities and numerical semigroups},
   JOURNAL = {Pacific J. Math.},
  FJOURNAL = {Pacific Journal of Mathematics},
    VOLUME = {218},
      YEAR = {2005},
    NUMBER = {2},
     PAGES = {379--398},
      ISSN = {0030-8730},
   MRCLASS = {20M14 (20M05 20M30)},
  MRNUMBER = {2218353},
MRREVIEWER = {Muhammad Zafrullah},
       DOI = {10.2140/pjm.2005.218.379},
       URL = {https://doi.org/10.2140/pjm.2005.218.379},
}

@article {RUB,
    AUTHOR = {Rosales, J. C. and Urbano-Blanco, J. M.},
     TITLE = {Opened modular numerical semigroups},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {306},
      YEAR = {2006},
    NUMBER = {2},
     PAGES = {368--377},
      ISSN = {0021-8693},
   MRCLASS = {20M10},
  MRNUMBER = {2271340},
MRREVIEWER = {Inessa Levi},
       DOI = {10.1016/j.jalgebra.2006.08.009},
       URL = {https://doi.org/10.1016/j.jalgebra.2006.08.009},
}

@article {RosalesVasco2008MIA,
    AUTHOR = {Rosales, J. C. and Vasco, P.},
     TITLE = {The smallest positive integer that is solution of a
              proportionally modular {D}iophantine inequality},
   JOURNAL = {Math. Inequal. Appl.},
  FJOURNAL = {Mathematical Inequalities \& Applications},
    VOLUME = {11},
      YEAR = {2008},
    NUMBER = {2},
     PAGES = {203--212},
      ISSN = {1331-4343},
   MRCLASS = {20M14 (11D75)},
  MRNUMBER = {2410272},
MRREVIEWER = {P. G. Trotter},
       DOI = {10.7153/mia-11-14},
       URL = {https://doi.org/10.7153/mia-11-14},
}

@article {gas-semigroups,
    AUTHOR = {D'Anna, Marco and Strazzanti, Francesco},
     TITLE = {Almost canonical ideals and {GAS} numerical semigroups},
   JOURNAL = {Comm. Algebra},
  FJOURNAL = {Communications in Algebra},
    VOLUME = {49},
      YEAR = {2021},
    NUMBER = {8},
     PAGES = {3534--3551},
      ISSN = {0092-7872},
   MRCLASS = {13H10 (20M14 20M25)},
  MRNUMBER = {4283166},
       DOI = {10.1080/00927872.2021.1900213},
       URL = {https://doi.org/10.1080/00927872.2021.1900213},
}

@article {RFMatrix,
    AUTHOR = {Moscariello, Alessio},
     TITLE = {On the type of an almost {G}orenstein monomial curve},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {456},
      YEAR = {2016},
     PAGES = {266--277},
      ISSN = {0021-8693},
   MRCLASS = {13H10 (14H45 20M14)},
  MRNUMBER = {3484144},
MRREVIEWER = {P. Schenzel},
       DOI = {10.1016/j.jalgebra.2016.02.019},
       URL = {https://doi.org/10.1016/j.jalgebra.2016.02.019},
}

@article {trace-ideal,
    AUTHOR = {Herzog, J\"{u}rgen and Hibi, Takayuki and Stamate, Dumitru I.},
     TITLE = {Canonical trace ideal and residue for numerical semigroup
              rings},
   JOURNAL = {Semigroup Forum},
  FJOURNAL = {Semigroup Forum},
    VOLUME = {103},
      YEAR = {2021},
    NUMBER = {2},
     PAGES = {550--566},
      ISSN = {0037-1912},
   MRCLASS = {20M14 (13A15 20M25)},
  MRNUMBER = {4305507},
       DOI = {10.1007/s00233-021-10205-x},
       URL = {https://doi.org/10.1007/s00233-021-10205-x},
}

@article {trace-canonical,
    AUTHOR = {Herzog, J\"{u}rgen and Hibi, Takayuki and Stamate, Dumitru I.},
     TITLE = {The trace of the canonical module},
   JOURNAL = {Israel J. Math.},
  FJOURNAL = {Israel Journal of Mathematics},
    VOLUME = {233},
      YEAR = {2019},
    NUMBER = {1},
     PAGES = {133--165},
      ISSN = {0021-2172},
   MRCLASS = {13H10 (05E40 06A11)},
  MRNUMBER = {4013970},
MRREVIEWER = {Yi-Huang Shen},
       DOI = {10.1007/s11856-019-1898-y},
       URL = {https://doi.org/10.1007/s11856-019-1898-y},
}

@article {homogeneous-ns,
    AUTHOR = {Jafari, Raheleh and Zarzuela Armengou, Santiago},
     TITLE = {Homogeneous numerical semigroups},
   JOURNAL = {Semigroup Forum},
  FJOURNAL = {Semigroup Forum},
    VOLUME = {97},
      YEAR = {2018},
    NUMBER = {2},
     PAGES = {278--306},
      ISSN = {0037-1912},
   MRCLASS = {20M14},
  MRNUMBER = {3852775},
MRREVIEWER = {Andreas Reinhart},
       DOI = {10.1007/s00233-018-9941-6},
       URL = {https://doi.org/10.1007/s00233-018-9941-6},
}

@article {dilatation,
    AUTHOR = {Barucci, V. and Strazzanti, F.},
     TITLE = {Dilatations of numerical semigroups},
   JOURNAL = {Semigroup Forum},
  FJOURNAL = {Semigroup Forum},
    VOLUME = {98},
      YEAR = {2019},
    NUMBER = {2},
     PAGES = {251--260},
      ISSN = {0037-1912},
   MRCLASS = {20M14},
  MRNUMBER = {3917961},
MRREVIEWER = {Attila Nagy},
       DOI = {10.1007/s00233-018-9922-9},
       URL = {https://doi.org/10.1007/s00233-018-9922-9},
}

@article{nearly-almost,
  title={Nearly Gorenstein vs almost Gorenstein affine monomial curves},
  author={Moscariello, Alessio and Strazzanti, Francesco},
  journal={Mediterranean Journal of Mathematics},
  volume={18},
  number={4},
  pages={1--14},
  year={2021},
  publisher={Springer}
}

@article{komatsu,
abstract = {In this paper, we give convenient formulas in order to obtain explicit expressions of a generalized Frobenius number called the p-Frobenius number as well as its related values. Here, for a non-negative integer p, the p-Frobenius number is the largest integer whose number of solutions of the linear diophantine equation in terms of positive integers {\$}{\$}a{\_}1,a{\_}2,{$\backslash$}ldots ,a{\_}k{\$}{\$}with {\$}{\$}{$\backslash$}gcd (a{\_}1,a{\_}2,{$\backslash$}ldots ,a{\_}k)=1{\$}{\$}is at most p. When {\$}{\$}p=0{\$}{\$}, the problem is reduced to the famous and classical linear Diophantine problem of Frobenius. 0-Frobenius number is the classical Frobenius number. Our formula is not only a natural extension of the existing classical formulas, but also has the great advantage that the explicit expressions of values such as the p-Frobenius and related numbers can be obtained systematically. The concept and formula of the weighted sum has been given recently. We also give a p-generalized formula for such weighted sums. The central role is the p-Ap{\'e}ry set, which is a generalization of the classical Ap{\'e}ry set.},
author = {Komatsu, Takao},
date = {2024/02/03},
date-added = {2024-02-03 17:45:40 +0100},
date-modified = {2024-02-03 17:45:40 +0100},
doi = {10.1007/s13398-024-01556-5},
id = {Komatsu2024},
isbn = {1579-1505},
journal = {Revista de la Real Academia de Ciencias Exactas, F{\'\i}sicas y Naturales. Serie A. Matem{\'a}ticas},
number = {2},
pages = {58},
title = {On the determination of p-Frobenius and related numbers using the p-Ap{\'e}ry set},
url = {https://doi.org/10.1007/s13398-024-01556-5},
volume = {118},
year = {2024},
bdsk-url-1 = {https://doi.org/10.1007/s13398-024-01556-5}}

@misc{SUER,
  doi = {10.48550/ARXIV.2207.13206},

  url = {https://arxiv.org/abs/2207.13206},

  author = {Süer, Meral},

  keywords = {Number Theory (math.NT), Commutative Algebra (math.AC), FOS: Mathematics, FOS: Mathematics, 20M14},

  title = {Irreducibility of Arf Numerical Semigroups},

  publisher = {arXiv},

  year = {2022},

  copyright = {Creative Commons Zero v1.0 Universal}
}

@article {araujo-neto,
    AUTHOR = {Ara\'{u}jo, Ant\'{o}nio and Neto, Orlando},
     TITLE = {Moduli of germs of {L}egendrian curves},
   JOURNAL = {Ann. Fac. Sci. Toulouse Math. (6)},
  FJOURNAL = {Annales de la Facult\'{e} des Sciences de Toulouse. Math\'{e}matiques.
              S\'{e}rie 6},
    VOLUME = {18},
      YEAR = {2009},
    NUMBER = {4},
     PAGES = {797--809},
      ISSN = {0240-2963},
   MRCLASS = {32S15 (58K60)},
  MRNUMBER = {2590388},
MRREVIEWER = {Patrick Popescu-Pampu},
       URL = {http://afst.cedram.org/item?id=AFST_2009_6_18_4_797_0},
}

quality91%

¤ Dauer der Verarbeitung: 0.38 Sekunden (vorverarbeitet) ¤

Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung ist noch experimentell.