Author:
Gasanova Oleksandra,Nicklasson Lisa
Abstract
AbstractWe introduce a family of toric algebras defined by maximal chains of a finite distributive lattice. Applying results on stable set polytopes, we conclude that every such algebra is normal and Cohen–Macaulay, and give an interpretation of its Krull dimension in terms of the combinatorics of the underlying lattice. When the lattice is planar, we show that the corresponding chain algebra is generated by a sortable set of monomials and is isomorphic to a Hibi ring of another finite distributive lattice. As a consequence, it has a defining toric ideal with a quadratic Gröbner basis, and its h-vector counts ascents in certain standard Young tableaux. If instead the lattice has dimension $$n>2$$
n
>
2
, we show that the defining ideal has minimal generators of degree at least n.
Funder
Wenner-Gren Stiftelserna
Knut och Alice Wallenbergs Stiftelse
Mälardalen University
Publisher
Springer Science and Business Media LLC
Subject
Discrete Mathematics and Combinatorics,Algebra and Number Theory