Quotients Of Coxeter Complexes And $P$-Partitions

This work deals with Coxeter complexes, a class of highly symmetrical triangulations of spheres and their quotients by symmetry subgroups. For certain subgroups, the author shows how the combinatorial theory of P-partitions may be used to analyse the quotient and how P-partitions and multipartite P-partitions may be extended to deal with more general classes of subgroups. Applications to combinatorics, topology, and invariant theory of finite groups are discussed.