Syzygies of polymatroidal ideals
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| author | Cid-Ruiz, Yairon Matherne, Jacob P. Shapiro, Anna |
| author_facet | Cid-Ruiz, Yairon Matherne, Jacob P. Shapiro, Anna |
| contents | 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 polymatroid. The cave polynomial gives a $K$-theoretic description of a polymatroid in the augmented $K$-ring of a multisymmetric lift. As applications, we settle two conjectures: one by Bandari, Bayati, and Herzog regarding polymatroidal ideals, and another by Castillo, Cid-Ruiz, Mohammadi, and Montaño regarding the Möbius support of a polymatroid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13153 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Syzygies of polymatroidal ideals Cid-Ruiz, Yairon Matherne, Jacob P. Shapiro, Anna Commutative Algebra Algebraic Geometry Combinatorics 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 polymatroid. The cave polynomial gives a $K$-theoretic description of a polymatroid in the augmented $K$-ring of a multisymmetric lift. As applications, we settle two conjectures: one by Bandari, Bayati, and Herzog regarding polymatroidal ideals, and another by Castillo, Cid-Ruiz, Mohammadi, and Montaño regarding the Möbius support of a polymatroid. |
| title | Syzygies of polymatroidal ideals |
| topic | Commutative Algebra Algebraic Geometry Combinatorics |
| url | https://arxiv.org/abs/2507.13153 |