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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.

Keywords

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

R2 v1 2026-07-01T09:01:00.992Z