Indispensable Hibi relations and Groebner Bases
Ayesha Asloob Qureshi
TL;DR
This paper classifies posets based on the indispensability of Hibi relations and the quadratic Groebner basis property of their associated Hibi and Rees rings, advancing understanding of their algebraic structures.
Contribution
It provides a complete classification of posets whose Hibi relations are indispensable and form quadratic Groebner bases, including Rees rings of Hibi ideals.
Findings
Classified posets with indispensable Hibi relations
Identified posets with quadratic Groebner bases for Hibi relations
Extended classifications to Rees rings of Hibi ideals
Abstract
In this paper we consider Hibi rings and Rees rings attached to a poset. We classify the ideal lattices of posets whose Hibi relations are indispensable and the ideal lattices of posets whose Hibi relations form a quadratic Groebner basis with respect to the rank lexicographic order. Similar classifications are obtained for Rees rings of Hibi ideals.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Polynomial and algebraic computation