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arXiv · 2602.14395

Partially ordered sets of distributive type and algebras with straightening laws

Takayuki Hibi·Seyed Amin Seyed Fakhari
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Abstract

A finite poset (partially ordered set) $P$ with ${\hat 0}$ is called of distributive type if every interval $[{\hat 0}, a]$, $a \in P$, of $P$ is a distributive lattice. From a viewpoint of ASL's (algebras with straightening laws), the join-meet toric ring on a finite distributive lattice is generalized to an ASL on a finite poset of distributive type. Our target is the questions when a finite poset of distributive lattice is Cohen--Macaulay and when the ASL on it is Gorenstein. We focus on a natural class of finite posets of distributive type and study various aspects of the above questions.

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Takayuki Hibi, Seyed Amin Seyed Fakhari. 2026-02-16. Partially ordered sets of distributive type and algebras with straightening laws. https://arxiv.org/abs/2602.14395

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