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#############################################################################
## This program is free software: you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation, either version 2 of the License, or
## (at your option) any later version.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
#W simpleAuts.gd Ruth Hoffmann
##
##
#Y Copyright (C) 2004-2015 School of Computer Science,
#Y University of St. Andrews, North Haugh,
#Y St. Andrews, Fife KY16 9SS, Scotland
##
################################################################################
##
#F GapGen(k)
##
## Returns the list of all lists of gap sizes possible for k.
##
## This is a helper function.
##
###########################
## NOT IN DOCUMENTATION ##
###########################
DeclareGlobalFunction( "GapGen" );
################################################################################
##
#F LengthBoundAut(aut,min,i,k)
##
## Constructs the automaton that accepts all words of aut of lengths between
## (and including) min and i.
##
DeclareGlobalFunction( "LengthBoundAut" );
################################################################################
##
#F ShiftAut(i,k)
##
## Returns the bounded class automaton but with the alphabet shifted (by value)
## up by i, to at most k. (excluding the empty perm and the perm of length 1)
##
DeclareGlobalFunction( "ShiftAut" );
################################################################################
##
#F NextGap(gap,rank)
##
## Knowing the gap sizes, and the rank of the point, NextGap calculates the next
## gap sizes when we add the point of that rank to the permutation.
##
DeclareGlobalFunction( "NextGap" );
################################################################################
##
#F GapAut(k)
##
## Returns the automaton, which has an alphabet of k, the set of states is the
## set of all possible gaps, the transition function is defined by the gap and
## the rank (see NextGap), the inital state is the emptyset of gap states, the
## accept states are the inital state and the state where the gap sizes is [0].
## This automaton is just an extended form of the bounded class automaton of k,
## the language is the same.
##
DeclareGlobalFunction( "GapAut" );
################################################################################
##
#F SumAut(sum,k)
##
## Constructs the automaton that accepts the prefixes of rank encoded permutations.
## The prefixes end in gap sizes which have total sum equal to sum.
##
DeclareGlobalFunction( "SumAut" );
################################################################################
##
#F GapSumAut(gap,sum,k)
##
## Constructs the automaton that accepts the prefixes of rank encoded permutations.
## The prefixes end with a gap of size gap and the sum of gap sizes before (or below
## in the plot) that gap has to equal to sum.
##
DeclareGlobalFunction( "GapSumAut" );
################################################################################
##
#F NonSimpleAut(k)
##
## Constructs the automaton that accepts all non-simple permutations with highest
## rank being k in their rank encoding.
##
DeclareGlobalFunction( "NonSimpleAut" );
################################################################################
##
#F SimplePermAut(k)
##
## Constructs the automaton of all simple permutations with rank encoding at
## most k.
##
DeclareGlobalFunction( "SimplePermAut" );
################################################################################
##
#F ExceptionalBoundedAutomaton(k)
##
## Returns the automaton that accepts exceptional permutations with rank
## encoding at most k.
##
DeclareGlobalFunction( "ExceptionalBoundedAutomaton" );
################################################################################
#### IsExceptionalPerm could possibly improved by building an automaton
#### that only accepts exceptional permutations of all lengths and then
#### check whether the input is accepted by such an automaton.
################################################################################
################################################################################
##
#F IsExceptionalPerm(perm)
##
## First checks whether perm has even length, then (if it does) compares it
## against the 4 different types of exceptional permutations in their rank
## encoding.
##
DeclareGlobalFunction( "IsExceptionalPerm" );
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