Standard multigraded Hibi rings and Cartwright-Sturmfels ideals
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916731605221376 |
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| author | Matsushita, Koji Tani, Koichiro |
| author_facet | Matsushita, Koji Tani, Koichiro |
| contents | In this paper, we introduce standard multigradings on Hibi rings, which are algebras arising from posets. We show that any standard multigrading on a Hibi ring that makes its defining ideal (called the Hibi ideal) homogeneous is induced by a chain of the underlying poset. After that, we calculate the multigraded Hilbert series of Hibi rings by generalizing the theory of $P$-partition and we compute the multidegree polynomials of Hibi rings. Furthermore, we characterize Hibi ideals that are Cartwright-Sturmfels ideals. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_06837 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Standard multigraded Hibi rings and Cartwright-Sturmfels ideals Matsushita, Koji Tani, Koichiro Commutative Algebra Combinatorics Primary: 13F65, Secondary: 13P10, 13D40, 05E40, 14M25 In this paper, we introduce standard multigradings on Hibi rings, which are algebras arising from posets. We show that any standard multigrading on a Hibi ring that makes its defining ideal (called the Hibi ideal) homogeneous is induced by a chain of the underlying poset. After that, we calculate the multigraded Hilbert series of Hibi rings by generalizing the theory of $P$-partition and we compute the multidegree polynomials of Hibi rings. Furthermore, we characterize Hibi ideals that are Cartwright-Sturmfels ideals. |
| title | Standard multigraded Hibi rings and Cartwright-Sturmfels ideals |
| topic | Commutative Algebra Combinatorics Primary: 13F65, Secondary: 13P10, 13D40, 05E40, 14M25 |
| url | https://arxiv.org/abs/2505.06837 |