Partially ordered sets of distributive type and algebras with straightening laws
Commutative Algebra
2026-02-17 v1 Combinatorics
Abstract
A finite poset (partially ordered set) with is called of distributive type if every interval , , of 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.
Cite
@article{arxiv.2602.14395,
title = {Partially ordered sets of distributive type and algebras with straightening laws},
author = {Takayuki Hibi and Seyed Amin Seyed Fakhari},
journal= {arXiv preprint arXiv:2602.14395},
year = {2026}
}