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Electronic Journal of Combinatorics
Article . 2023 . Peer-reviewed
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Nearly Gorenstein Polytopes

Nearly Gorenstein polytopes
descriptionPublicationkeyboard_double_arrow_right Article , Preprint 15 Dec 2023Embargo end date: 01 Jan 2023Publisher:The Electronic Journal of CombinatoricsJournal:The Electronic Journal of Combinatorics, volume 30 (eissn: 1077-8926, Copyright policy )
Authors: Thomas Hall; Max Kölbl; Koji Matsushita; Sora Miyashita;

doi: 10.37236/12017 , 10.48550/arxiv.2303.13084

arXiv: 2303.13084

Nearly Gorenstein Polytopes

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.

Related Organizations
Keywords

52B20, 13H10, 14M25, Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry), Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Toric varieties, Newton polyhedra, Okounkov bodies, Mathematics - Commutative Algebra, Commutative Algebra (math.AC)

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    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 5
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Top 10%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    		 Top 10%
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
5
Top 10%
Average
Top 10%
Green
gold