Rank Bounded Hibi Subrings for Planar Distributive Lattices

Abstract

Let $L$ be a distributive lattice and $R[L]$ the associated Hibi ring. We show that if $L$ is planar, then any bounded Hibi subring of $R[L]$ has a quadratic Gröbner basis. We characterize all planar distributive lattices $L$ for which any proper rank bounded Hibi subring of $R[L]$ has a linear resolution. Moreover, if $R[L]$ is linearly related for a lattice $L$, we find all the rank bounded Hibi subrings of $R[L]$ which are linearly related too.

Accepted in Mathematical Communications

References in corpus (1)

• Ideals generated by 2-minors, collection of cells and stack polyominoes