English

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) PP with 0^{\hat 0} is called of distributive type if every interval [0^,a][{\hat 0}, a], aPa \in P, of PP 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.

Keywords

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}
}