Combinatorics# Contents# Partitions Permutations Generators Permutation Groups Polyhedron Prufer Sequences Subsets Gray Code Named Groups Nilpotent, Abelian and Cyclic Numbers Utilities Group constructors Test Utilities Tensor Canonicalization Finitely Presented Groups Introduction The Construction of Finitely Presented Groups Free Groups and Words Coset Enumeration: The Todd-Coxeter Algorithm Subgroups of Finite Index Constructing a presentation for a subgroup Bibliography Polycyclic Groups Introduction The Construction of Polycyclic Groups The Construction of Collector Computation of Polycyclic Presentation Computation of Exponent Vector Bibliography