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james-d-mitchell committed Jan 15, 2024
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2 changes: 1 addition & 1 deletion PackageInfo.g
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#############################################################################
##
## PackageInfo.g Smallsemi - a GAP library of semigroups
## Copyright (C) 2008-2015 Andreas Distler & James D. Mitchell
## Copyright (C) 2008-2024 Andreas Distler & James D. Mitchell
##
## Licensing information can be found in the README file of this package.
##
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60 changes: 28 additions & 32 deletions gap/3nil.gd
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#############################################################################
##

###########################################################################
##
## <#GAPDoc Label="Nr3NilpotentSemigroups">
## <ManSection>
## <Func Name="Nr3NilpotentSemigroups" Arg="n[, type]"/>
## <Description>
## returns the number of 3-nilpotent semigroups on a set with <A>n</A>
## elements. If the optional argument <A>type</A> is given it must be one
## of <C>"UpToEquivalence", "UpToIsomorphism", "SelfDual", "Commutative",
## "Labelled", "Labelled-Commutative"</C>.
## The number will be returned for the respective type of semigroup.
## By default <A>type</A> is <C>"UpToEquivalence"</C>.
## <P/>
## The function implements the formulae calculating the number of
## 3-nilpotent semigroups developed in <Cite Key="Dis10"/>
## <Example><![CDATA[
## gap> Nr3NilpotentSemigroups( 4 );
## 8
## gap> Nr3NilpotentSemigroups( 9, "UpToIsomorphism" );
## 105931872028455
## gap> Nr3NilpotentSemigroups( 9, "Labelled" );
## 38430603831264883632
## gap> Nr3NilpotentSemigroups( 16, "SelfDual" );
## 4975000837941847814744710290469890455985530
## gap> Nr3NilpotentSemigroups( 19, "Commutative" );
## 12094270656160403920767935604624748908993169949317454767617795
## ]]></Example> <!-- enums.tst -->
## </Description>
## </ManSection>
## <#/GAPDoc>
##

# <#GAPDoc Label="Nr3NilpotentSemigroups">
# <ManSection>
# <Func Name="Nr3NilpotentSemigroups" Arg="n[, type]"/>
# <Description>
# returns the number of 3-nilpotent semigroups on a set with <A>n</A>
# elements. If the optional argument <A>type</A> is given it must be one
# of <C>"UpToEquivalence", "UpToIsomorphism", "SelfDual", "Commutative",
# "Labelled", "Labelled-Commutative"</C>.
# The number will be returned for the respective type of semigroup.
# By default <A>type</A> is <C>"UpToEquivalence"</C>.
# <P/>
# The function implements the formulae calculating the number of
# 3-nilpotent semigroups developed in <Cite Key="Dis10"/>
# <Example><![CDATA[
# gap> Nr3NilpotentSemigroups( 4 );
# 8
# gap> Nr3NilpotentSemigroups( 9, "UpToIsomorphism" );
# 105931872028455
# gap> Nr3NilpotentSemigroups( 9, "Labelled" );
# 38430603831264883632
# gap> Nr3NilpotentSemigroups( 16, "SelfDual" );
# 4975000837941847814744710290469890455985530
# gap> Nr3NilpotentSemigroups( 19, "Commutative" );
# 12094270656160403920767935604624748908993169949317454767617795
# ]]></Example> <!-- enums.tst -->
# </Description>
# </ManSection>
# <#/GAPDoc>
DeclareGlobalFunction("Nr3NilpotentSemigroups");
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