Three Combinatorial Algorithms for the Cave Polynomial of a Polymatroid

Abstract

The cave polynomial of a polymatroid was recently introduced and used to study the syzygies of polymatroidal ideals. We study the combinatorial relationships between three formulas for the cave polynomial. As an application, we interpret the Snapper polynomial in terms of these three formulas.

arXiv comment12 pages, to appear in Proceedings of the AMS