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arXiv · 2505.06837

Standard multigraded Hibi rings and Cartwright-Sturmfels ideals

Koji Matsushita·Koichiro Tani
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Abstract

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.

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Koji Matsushita, Koichiro Tani. 2025-05-11. Standard multigraded Hibi rings and Cartwright-Sturmfels ideals. https://arxiv.org/abs/2505.06837

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