Rank bounded Hibi subrings for planar distributive lattices

Rida Irfan; Nadia Shoukat

Vol. 24 No. 2 (2019)

Regular Articles

Rank bounded Hibi subrings for planar distributive lattices

Published 2019-07-23

Rida Irfan
Nadia Shoukat

Rida Irfan
COMSATS Univesity Islamabad, Sahiwal Campus, Pakistan.

Nadia Shoukat
Abdus Salam School of Mathematical Sciences, GC University, Lahore Pakistan.

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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 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

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Author Biography

Rida Irfan

Assistant Professor,

Department of Mathematics

Nadia Shoukat

PhD Scholar