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arXiv · 1901.06690

Rank Bounded Hibi Subrings for Planar Distributive Lattices

Rida Irfan·Nadia Shoukat
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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 Gr\"obner 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.

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Rida Irfan, Nadia Shoukat. 2019-01-20. Rank Bounded Hibi Subrings for Planar Distributive Lattices. https://arxiv.org/abs/1901.06690

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