Toric rings and ideals of nested configurations
Hidefumi Ohsugi, Takayuki Hibi
TL;DR
This paper investigates the algebraic properties of toric rings and ideals derived from nested configurations, focusing on normality and Gr"obner bases, with applications to smooth transportation polytopes.
Contribution
It introduces new algebraic insights into nested configuration toric rings and ideals, especially regarding their normality and Gr"obner bases, with applications to transportation polytopes.
Findings
Characterization of normality conditions for toric rings from nested configurations
Development of Gr"obner basis techniques for associated toric ideals
Application to understanding smooth 3x3 transportation polytopes
Abstract
The toric ring together with the toric ideal arising from a nested configuration is studied, with particular attention given to the algebraic study of normality of the toric ring as well as the Gr\"obner bases of the toric ideal. One of the combinatorial applications of these algebraic findings leads to insights on smooth transportation polytopes.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic Geometry and Number Theory · Polynomial and algebraic computation