Three Combinatorial Algorithms for the Cave Polynomial of a Polymatroid
Combinatorics
2026-01-13 v1 Commutative Algebra
Algebraic Geometry
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.
Cite
@article{arxiv.2601.07697,
title = {Three Combinatorial Algorithms for the Cave Polynomial of a Polymatroid},
author = {Anna Shapiro},
journal= {arXiv preprint arXiv:2601.07697},
year = {2026}
}
Comments
11 pages