Rank bounded Hibi subrings for planar distributive lattices

Rida Irfan, Nadia Shoukat


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 Grobner 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.


Rank bounded Hibi Subrings; Linear resolution; Linear syzygies

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ISSN: 1331-0623 (Print), 1848-8013 (Online)