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<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<!-- %% -->
<!-- %A combinat.xml GAP documentation Martin Schönert -->
<!-- %A Alexander Hulpke -->
<!-- %% -->
<!-- %% -->
<!-- %Y (C) 1998 School Math and Comp. Sci., University of St Andrews, Scotland -->
<!-- %Y Copyright (C) 2002 The GAP Group -->
<!-- %% -->
<Chapter Label="Combinatorics">
<Heading>Combinatorics</Heading>
This chapter describes functions that deal with combinatorics.
We mainly concentrate on two areas.
One is about <E>selections</E>,
that is the ways one can select elements from a set.
The other is about <E>partitions</E>,
that is the ways one can partition a set into the union of pairwise disjoint
subsets.
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Combinatorial Numbers">
<Heading>Combinatorial Numbers</Heading>
<#Include Label="Factorial">
<#Include Label="Binomial">
<#Include Label="Bell">
<#Include Label="Bernoulli">
<#Include Label="Stirling1">
<#Include Label="Stirling2">
</Section>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Combinations, Arrangements and Tuples">
<Heading>Combinations, Arrangements and Tuples</Heading>
<#Include Label="Combinations">
<#Include Label="IteratorOfCombinations">
<#Include Label="NrCombinations">
<#Include Label="Arrangements">
<#Include Label="NrArrangements">
<#Include Label="UnorderedTuples">
<#Include Label="NrUnorderedTuples">
<#Include Label="Tuples">
<#Include Label="EnumeratorOfTuples">
<#Include Label="IteratorOfTuples">
<#Include Label="NrTuples">
<#Include Label="PermutationsList">
<#Include Label="NrPermutationsList">
<#Include Label="Derangements">
<#Include Label="NrDerangements">
<#Include Label="PartitionsSet">
<#Include Label="NrPartitionsSet">
<#Include Label="Partitions">
<#Include Label="IteratorOfPartitions">
<#Include Label="IteratorOfPartitionsSet">
<#Include Label="NrPartitions">
<#Include Label="OrderedPartitions">
<#Include Label="NrOrderedPartitions">
<#Include Label="PartitionsGreatestLE">
<#Include Label="PartitionsGreatestEQ">
<#Include Label="RestrictedPartitions">
<#Include Label="NrRestrictedPartitions">
<#Include Label="SignPartition">
<#Include Label="AssociatedPartition">
<#Include Label="PowerPartition">
<#Include Label="PartitionTuples">
<#Include Label="NrPartitionTuples">
<#Include Label="BetaSet">
</Section>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Fibonacci and Lucas Sequences">
<Heading>Fibonacci and Lucas Sequences</Heading>
<#Include Label="Fibonacci">
<#Include Label="Lucas">
</Section>
<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Permanent of a Matrix">
<Heading>Permanent of a Matrix</Heading>
<#Include Label="Permanent">
</Section>
</Chapter>
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