We consider a continuous space which models the set of all phylogenetic trees having a fixed set of leaves. This space has a natural metric of nonpositive curvature, giving a way of measuring… Expand

This paper generalizes the Dehn-Sommerville equations for simplicial spheres to related classes of objects. The underlying motivation is to understand the combinatorial structure of arbitrary… Expand

It is shown that several cases in which the Hirsch conjecture has been verified can be handled by these methods, which also give the shellability of a number of simplicial complexes of combinatorial interest.Expand

For A a triangulated d-dimensional region in Rd, let Sr (A) denote the vector space of all cr functions F on A that, restricted to any simplex in A, are given by polynomials of degree at most m. We… Expand

In this note, cost allocation procedures are considered and it is shown that there is exactly one such procedure which possesses four desirable properties.Expand

For convex d-polytope P let ft{P) equal the number of faces of P of dimension i, 0 < i < d 1. f(P) = (f0(P)9 . . . , fd^QP)) is called the f vector of P An important combinatorial problem is the… Expand