Regularity of Join-meet Ideals of Distributive Lattices

Abstract

Let $L$ be a distributive lattice and $R(L)$ the associated Hibi ring. We compute reg $R(L)$ when $L$ is  a planar  lattice and give  bounds for reg $R(L)$ when $L$ is non-planar, in terms of the combinatorial data of $L.$  As a consequence, we characterize the distributive lattices $L$ for which the associated Hibi ring has a linear resolution.