Nearly Gorenstein Polytopes
Thomas Hall, Max K\"olbl, Koji Matsushita, Sora Miyashita
TL;DR
This paper investigates the nearly Gorenstein property of Ehrhart rings from lattice polytopes, providing conditions, construction methods, and characterizations for specific classes of polytopes.
Contribution
It offers new necessary and sufficient conditions for nearly Gorenstein Ehrhart rings and characterizes this property for (0,1)-polytopes, edge polytopes, and graphic matroids.
Findings
Established conditions for nearly Gorensteinness of Ehrhart rings.
Developed an efficient construction method for nearly Gorenstein polytopes.
Characterized nearly Gorensteinness in specific polytope classes.
Abstract
In this paper, we study nearly Gorensteinness of Ehrhart rings arising from lattice polytopes. We give necessary conditions and sufficient conditions on lattice polytopes for their Ehrhart rings to be nearly Gorenstein. Using this, we give an efficient method for constructing nearly Gorenstein polytopes. Moreover, we determine the structure of nearly Gorenstein (0, 1)-polytopes and characterise nearly Gorensteinness of edge polytopes and graphic matroids.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Advanced Combinatorial Mathematics · Algebraic structures and combinatorial models