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<h3>References</h3>


<p><a id="biBAraujo2015aa" name="biBAraujo2015aa"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>ABMS15</span>]   <b class='BibAuthor'>Araújo, J., Bentz, W., Mitchell, J. D. and Schneider, C.</b>,
 <i class='BibTitle'>The rank of the semigroup of transformations stabilising a partition
      of a finite set</i>,
 <span class='BibJournal'>Math. Proc. Camb. Phil. Soc.</span>,
 <em class='BibVolume'>159</em>
 (<span class='BibYear'>2015</span>),
 <span class='BibPages'>339 - 353</span>.
</p>


<p><a id="biBAnagnostopoulou-Merkouri2021aa" name="biBAnagnostopoulou-Merkouri2021aa"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>AMM23</span>]   <b class='BibAuthor'>Anagnostopoulou-Merkouri, M., Mesyan, Z. and Mitchell, J. D.</b>,
 <i class='BibTitle'>Properties of congruence lattices of graph inverse semigroups</i>,
 <span class='BibJournal'>International Journal of Algebra and Computation</span>
 (<span class='BibYear'>2023</span>).
</p>


<p><a id="biBauinger2012krohn" name="biBauinger2012krohn"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Aui12</span>]   <b class='BibAuthor'>Auinger, K.</b>,
 <i class='BibTitle'>Krohn–Rhodes complexity of Brauer type
      semigroups</i>,
 <span class='BibJournal'>Portugaliae Mathematica</span>,
 <em class='BibVolume'>69</em> (<span class='BibNumber'>4</span>)
 (<span class='BibYear'>2012</span>),
 <span class='BibPages'>341–360</span>.
</p>


<p><a id="biBBrouwer2015aa" name="biBBrouwer2015aa"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>BDF15</span>]   <b class='BibAuthor'>Brouwer, A. E., Draisma, J. and Frenk, B. J.</b>,
<a href="https://dx.doi.org/10.1007/s00454-015-9666-1"><i class='BibTitle'>Lossy Gossip and Composition of Metrics</i></a>,
 <span class='BibJournal'>Discrete & Computational Geometry</span>,
 <em class='BibVolume'>53</em> (<span class='BibNumber'>4</span>)
 (<span class='BibYear'>2015</span>),
 <span class='BibPages'>890–913</span>.
</p>


<p><a id="biBBacelli1992aa" name="biBBacelli1992aa"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>BFCGOGJ92</span>]   <b class='BibAuthor'>Baccelli F. Cohen G. Olsder G. J., Q. J. P.</b>,
 <i class='BibTitle'>Synchronisation and Linearity: An Algebra for
      Discrete Event Systems</i>,
 <span class='BibPublisher'>Wiley</span>
 (<span class='BibYear'>1992</span>).
</p>


<p><a id="biBBurrell2016aa" name="biBBurrell2016aa"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Bur16</span>]   <b class='BibAuthor'>Burrell, S. A.</b>,
 <i class='BibTitle'>The Order Problem for Natural and Tropical Matrix
      Semigroups</i>,
 <span class='BibType'>MMath project</span>,
 <span class='BibSchool'>University of St Andrews</span>,
 <span class='BibAddress'>United Kingdom</span>
 (<span class='BibYear'>2016</span>).
</p>


<p><a id="biBClifford1977aa" name="biBClifford1977aa"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>CP77</span>]   <b class='BibAuthor'>Clifford, A. H. and Petrich, M.</b>,
<a href="http://dx.doi.org/10.1016/0021-8693(77)90383-0"><i class='BibTitle'>Some classes of completely regular semigroups</i></a>,
 <span class='BibJournal'>Journal of Algebra</span>,
 <em class='BibVolume'>46</em> (<span class='BibNumber'>2</span>)
 (<span class='BibYear'>1977</span>),
 <span class='BibPages'>462--480</span>.
</p>


<p><a id="biBDonoven2018aa" name="biBDonoven2018aa"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>DMW18</span>]   <b class='BibAuthor'>Donoven, C., Mitchell, J. D. and Wilson, W. A.</b>,
 <i class='BibTitle'>Computing maximal subsemigroups of a finite semigroup</i>,
 <span class='BibJournal'>Journal of Algebra</span>,
 <em class='BibVolume'>505</em>
 (<span class='BibYear'>2018</span>),
 <span class='BibPages'>559-596</span>.
</p>


<p><a id="biBEast2019aa" name="biBEast2019aa"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Eas19</span>]   <b class='BibAuthor'>East, J.</b>,
<a href="https://www.sciencedirect.com/science/article/pii/S0022404918301403"><i class='BibTitle'>Presentations for rook partition monoids and algebras and their
      singular ideals</i></a>,
 <span class='BibJournal'>J. Pure and Applied Algebra</span>,
 <em class='BibVolume'>223</em>
 (<span class='BibYear'>2019</span>),
 <span class='BibPages'>1097-1122</span>.
</p>


<p><a id="biBMitchell2019aa" name="biBMitchell2019aa"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>EEMP19</span>]   <b class='BibAuthor'>East, J., Egri-Nagy, A., Mitchell, J. D. and Péresse, Y.</b>,
<a href="https://www.sciencedirect.com/science/article/pii/S0747717118300087"><i class='BibTitle'>Computing finite semigroups</i></a>,
 <span class='BibJournal'>J. Symbolic Computation</span>,
 <em class='BibVolume'>92</em>
 (<span class='BibYear'>2019</span>),
 <span class='BibPages'>110 - 155</span>.
</p>


<p><a id="biBKacie2009aa" name="biBKacie2009aa"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Far09</span>]   <b class='BibAuthor'>Farlow, K. G.</b>,
 <i class='BibTitle'>Max-Plus Algebra</i>,
 <span class='BibType'>Master's thesis</span>,
 <span class='BibSchool'>Virginia Polytechnic Institute and State University</span>,
 <span class='BibAddress'>United States</span>
 (<span class='BibYear'>2009</span>).
</p>


<p><a id="biBFitzgerald1998aa" name="biBFitzgerald1998aa"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>FL98</span>]   <b class='BibAuthor'>Fitzgerald, D. G. and Leech, J.</b>,
 <i class='BibTitle'>Dual symmetric inverse monoids and representation theory</i>,
 <span class='BibJournal'>J. Austral. Math. Soc. A</span>,
 <em class='BibVolume'>64</em>
 (<span class='BibYear'>1998</span>),
 <span class='BibPages'>345-67</span>.
</p>


<p><a id="biBFroidure1997aa" name="biBFroidure1997aa"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>FP97</span>]   <b class='BibAuthor'>Froidure, V. and Pin, J.-E.</b>,
 <i class='BibTitle'>Algorithms for computing finite semigroups</i>,
  in  <i class='BibBooktitle'>Foundations of computational mathematics (Rio de
      Janeiro, 1997)</i>,
 <span class='BibPublisher'>Springer</span>,
 <span class='BibAddress'>Berlin</span>
 (<span class='BibYear'>1997</span>),
 <span class='BibPages'>112–126</span>.
</p>


<p><a id="biBGaubert1996aa" name="biBGaubert1996aa"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Gau96</span>]   <b class='BibAuthor'>Gaubert, S.</b>,
 <i class='BibTitle'>On the Burnside problem for Semigroups of
      Matrices over the (max, +) Algebra</i>,
 <span class='BibJournal'>Semigroup Forum</span>,
 <em class='BibVolume'>5</em>
 (<span class='BibYear'>1996</span>),
 <span class='BibPages'>271-292</span>.
</p>


<p><a id="biBGraham1968aa" name="biBGraham1968aa"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>GGR68</span>]   <b class='BibAuthor'>Graham, N., Graham, R. and Rhodes, J.</b>,
 <i class='BibTitle'>Maximal subsemigroups of finite semigroups</i>,
 <span class='BibJournal'>J. Combinatorial Theory</span>,
 <em class='BibVolume'>4</em>
 (<span class='BibYear'>1968</span>),
 <span class='BibPages'>203–209</span>.
</p>


<p><a id="biBGraham1968Graph" name="biBGraham1968Graph"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Gra68</span>]   <b class='BibAuthor'>Graham, R.</b>,
 <i class='BibTitle'>On finite 0-simple semigroups and graph theory</i>,
 <span class='BibJournal'>Mathematical systems theory</span>,
 <em class='BibVolume'>2</em> (<span class='BibNumber'>4</span>)
 (<span class='BibYear'>1968</span>),
 <span class='BibPages'>325–339</span>.
</p>


<p><a id="biBGrood2006aa" name="biBGrood2006aa"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Gro06</span>]   <b class='BibAuthor'>Grood, C.</b>,
<a href="https://dx.doi.org/10.1016/j.jcta.2005.03.006"><i class='BibTitle'>The rook partition algebra</i></a>,
 <span class='BibJournal'>J. Combin. Theory Ser. A</span>,
 <em class='BibVolume'>113</em> (<span class='BibNumber'>2</span>)
 (<span class='BibYear'>2006</span>),
 <span class='BibPages'>325–351</span>.
</p>


<p><a id="biBHowie1995aa" name="biBHowie1995aa"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>How95</span>]   <b class='BibAuthor'>Howie, J. M.</b>,
 <i class='BibTitle'>Fundamentals of semigroup theory</i>,
 <span class='BibPublisher'>The Clarendon Press Oxford University Press</span>,
 <span class='BibSeries'>London Mathematical Society Monographs. New Series</span>,
 <em class='BibVolume'>12</em>,
 <span class='BibAddress'>New York</span>
 (<span class='BibYear'>1995</span>),
 <span class='BibPages'>x+351 pages</span><br />
(<span class='BibNote'>Oxford Science Publications</span>).
</p>


<p><a id="biBHalverson2005PartitionAlgebras" name="biBHalverson2005PartitionAlgebras"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>HR05</span>]   <b class='BibAuthor'>Halverson, T. and Ram, A.</b>,
 <i class='BibTitle'>Partition algebras</i>,
 <span class='BibJournal'>European Journal of Combinatorics</span>,
 <span class='BibPublisher'>Elsevier</span>,
 <em class='BibVolume'>26</em> (<span class='BibNumber'>6</span>)
 (<span class='BibYear'>2005</span>),
 <span class='BibPages'>869–921</span>.
</p>


<p><a id="biBJunttilaKaski" name="biBJunttilaKaski"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>JK07</span>]   <b class='BibAuthor'>Junttila, T. and Kaski, P.</b> (<span class='BibEditor'>Applegate, D., Brodal, G. S., Panario, D. and Sedgewick, R.</span>, Eds.),
 <i class='BibTitle'>Engineering an efficient canonical labeling tool for large and sparse
      graphs</i>,
  in  <i class='BibBooktitle'>Proceedings of the Ninth Workshop on Algorithm Engineering and
      Experiments and the Fourth Workshop on Analytic Algorithms and
      Combinatorics</i>,
 <span class='BibPublisher'>SIAM</span>
 (<span class='BibYear'>2007</span>),
 <span class='BibPages'>135–149</span>.
</p>


<p><a id="biBKudryavtseva2011aa" name="biBKudryavtseva2011aa"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>KM11</span>]   <b class='BibAuthor'>Kudryavtseva, G. and Maltcev, V.</b>,
<a href="https://dx.doi.org/10.5486/PMD.2011.4375"><i class='BibTitle'>Two generalisations of the symmetric inverse semigroups</i></a>,
 <span class='BibJournal'>Publ. Math. Debrecen</span>,
 <em class='BibVolume'>78</em> (<span class='BibNumber'>2</span>)
 (<span class='BibYear'>2011</span>),
 <span class='BibPages'>253–282</span>.
</p>


<p><a id="biBKudryavtseva2015aa" name="biBKudryavtseva2015aa"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>KMU15</span>]   <b class='BibAuthor'>Kudryavtseva, G., Maltcev, V. and Umar, A.</b>,
<a href="https://dx.doi.org/10.1080/00927872.2013.876031"><i class='BibTitle'>Presentation for the partial dual symmetric inverse monoid</i></a>,
 <span class='BibJournal'>Comm. Algebra</span>,
 <em class='BibVolume'>43</em> (<span class='BibNumber'>4</span>)
 (<span class='BibYear'>2015</span>),
 <span class='BibPages'>1621–1639</span>.
</p>


<p><a id="biBMartin2011aa" name="biBMartin2011aa"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>MM13</span>]   <b class='BibAuthor'>Martin, P. and Mazorchuk, V.</b>,
<a href="https://www.mscand.dk/article/view/15480"><i class='BibTitle'>Partitioned binary relations</i></a>,
 <span class='BibJournal'>Mathematica Scandinavica</span>,
 <em class='BibVolume'>113</em>
 (<span class='BibYear'>2013</span>),
 <span class='BibPages'>30-52</span>.
</p>


<p><a id="biBMesyan2016" name="biBMesyan2016"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>MM16</span>]   <b class='BibAuthor'>Mesyan, Z. and Mitchell, J. D.</b>,
<a href="https://doi.org/10.1007/s00233-016-9793-x"><i class='BibTitle'>The structure of a graph inverse semigroup</i></a>,
 <span class='BibJournal'>Semigroup Forum</span>,
 <span class='BibPublisher'>Springer Nature</span>,
 <em class='BibVolume'>93</em> (<span class='BibNumber'>1</span>)
 (<span class='BibYear'>2016</span>),
 <span class='BibPages'>111–130</span>.
</p>


<p><a id="biBPetrich1970aa" name="biBPetrich1970aa"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Pet70</span>]   <b class='BibAuthor'>Petrich, M.</b>,
<a href="https://doi.org/10.1007/BF02573051"><i class='BibTitle'>The translational hull in semigroups and rings</i></a>,
 <span class='BibJournal'>Semigroup Forum</span>,
 <em class='BibVolume'>1</em> (<span class='BibNumber'>1</span>)
 (<span class='BibYear'>1970</span>),
 <span class='BibPages'>283--360</span>.
</p>


<p><a id="biBRadoszewski2010aa" name="biBRadoszewski2010aa"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>RR10</span>]   <b class='BibAuthor'>Radoszewski, J. and Rytter, W.</b> (<span class='BibEditor'>van Leeuwen, J., Muscholl, A., Peleg, D., Pokorný, J. and Rumpe, B.</span>, Eds.),
 <i class='BibTitle'>Efficient Testing of Equivalence of Words in a Free Idempotent Semigroup</i>,
 <span class='BibJournal'>SOFSEM 2010: Theory and Practice of Computer Science</span>,
 <span class='BibPublisher'>Springer Berlin Heidelberg</span>,
 <span class='BibAddress'>Berlin, Heidelberg</span>
 (<span class='BibYear'>2010</span>),
 <span class='BibPages'>663--671</span>.
</p>


<p><a id="biBSchein1992aa" name="biBSchein1992aa"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Sch92</span>]   <b class='BibAuthor'>Schein, B. M.</b>,
 <i class='BibTitle'>The minimal degree of a finite inverse semigroup</i>,
 <span class='BibJournal'>Trans. Amer. Math. Soc.</span>,
 <em class='BibVolume'>333</em> (<span class='BibNumber'>2</span>)
 (<span class='BibYear'>1992</span>),
 <span class='BibPages'>877–888</span>.
</p>


<p><a id="biBSimon1978aa" name="biBSimon1978aa"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Sim78</span>]   <b class='BibAuthor'>Simon, I.</b>,
<a href="https://dx.doi.org/10.1109/SFCS.1978.21"><i class='BibTitle'>Limited Subsets of a Free Monoid</i></a>,
  in  <i class='BibBooktitle'>Proceedings of the 19th Annual Symposium on Foundations of
      Computer Science</i>,
 <span class='BibPublisher'>IEEE Computer Society</span>,
 <span class='BibSeries'>SFCS '78</span>,
 <span class='BibAddress'>Washington, DC, USA</span>
 (<span class='BibYear'>1978</span>),
 <span class='BibPages'>143–150</span>.
</p>


<p><a id="biBWang2019aa" name="biBWang2019aa"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Wan19</span>]   <b class='BibAuthor'>Wang, Z.-P.</b>,
<a href="https://doi.org/10.1016/j.jalgebra.2019.06.020"><i class='BibTitle'>Congruences on Graph Inverse Semigroups</i></a>,
 <span class='BibJournal'>Journal of Algebra</span>,
 <span class='BibPublisher'>Elsevier {BV}</span>,
 <em class='BibVolume'>534</em>
 (<span class='BibYear'>2019</span>),
 <span class='BibPages'>51--64</span>.
</p>

<p> </p>


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