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arXiv · 2601.07697

Three Combinatorial Algorithms for the Cave Polynomial of a Polymatroid

Anna Shapiro
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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.

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Anna Shapiro. 2026-07-20. Three Combinatorial Algorithms for the Cave Polynomial of a Polymatroid. https://arxiv.org/abs/2601.07697

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