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math.AC2025
Standard multigraded Hibi rings and Cartwright-Sturmfels ideals
Koji Matsushita, Koichiro Tani
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 defin…
math.AC2025
Khovanskii bases of subalgebras arising from finite distributive lattices
Akihiro Higashitani, Koji Matsushita, Koichiro Tani
The notion of Khovanskii bases was introduced by Kaveh and Manon. It is a generalization of the notion of SAGBI bases for a subalgebra of polynomials. The notion of SAGBI bases was…
math.AC2024
Dual -signatures of Veronese subrings and Segre products of polynomial rings
Koji Matsushita
In this paper, we compute the dual -signatures of certain toric rings by using combinatorial techniques. Specifically, we calculate the dual -signatures of Veronese subrings…