Finite lattices and Gr\"obner bases
J\"urgen Herzog, Takayuki Hibi
TL;DR
This paper explores the relationship between finite lattices and Gr"obner bases of binomial ideals, providing characterizations of finite and planar distributive lattices through algebraic and combinatorial methods.
Contribution
It offers new characterizations of finite and planar distributive lattices using Gr"obner bases and initial ideals, linking lattice theory with computational algebra.
Findings
Characterization of finite distributive lattices via Gr"obner bases
Characterization of planar distributive lattices using initial ideals
Insights into binomial ideals associated with finite lattices
Abstract
Gr\"obner bases of binomial ideals arising from finite lattices will be studied. In terms of Gr\"obner bases and initial ideals, a characterization of finite distributive lattices as well as planar distributive lattices will be given.
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Taxonomy
TopicsPolynomial and algebraic computation · Advanced Numerical Analysis Techniques · Commutative Algebra and Its Applications