Original scientific paper

Rank bounded Hibi subrings for planar distributive lattices

Rida Irfan orcid.org/0000-0001-5793-3598 ; Department of Mathematics, COMSATS University Islamabad, Sahiwal Campus, Sahiwal, Pakistan
Nadia Shoukat ; Abdus Salam School of Mathematical Sciences, GC University, Lahore 68-B, New Muslim Town, Lahore, Pakistan

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 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.

Keywords

Rank bounded Hibi Subrings; Linear resolution; Linear syzygies

Hrčak ID:

227066

URI

https://hrcak.srce.hr/227066

Publication date:

25.10.2019.

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