The concept of shellability of complexes is generalized by deleting the requirement of purity (i.e., that all maximal faces have the same dimension). The usefulness of this level of generality was… (More)

In this paper we study shellable posets (partially ordered sets), that is, finite posets such that the simplicial complex of chains is shellable. It is shown that all admissible lattices (including… (More)

We analyze the following (solitaire) game: each node of a graph contains a pile of chips, and a move consists of selecting a node with at least as many chips on it as its degree, and let it send one… (More)

We study combinatorial properties, such as inversion table, weak order and Bruhat order, for certain infinite permutations that realize the affine Coxeter group Ãn.

We consider subsets of the symmetric group for which the inversion index and major index are equally distributed. Our results extend and unify results of MacMahon, Foata, and Schtitzenberger, and the… (More)

A Cohen--Macaulay conaplex is said to be balanced of type a = (aa, a, . . . . . a.~) if ils vertices can be cnlored using s colors so that every maximal face gets exactly a, vertices of the i:th… (More)

We present an algorithm based on bistellar operations that provides a useful tool for the construction of simplicial manifolds with few vertices. As an example, we obtain a 16-vertex triangulation of… (More)