2 papers
math.CO2026
Three Combinatorial Algorithms for the Cave Polynomial of a Polymatroid
Anna Shapiro
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…
math.AC2025
Syzygies of polymatroidal ideals
Yairon Cid-Ruiz, Jacob P. Matherne, Anna Shapiro
We introduce the cave polynomial of a polymatroid and show that it yields a valuative function on polymatroids. The support of this polynomial after homogenization is again a polym…