The Universal Gröbner Basis of a Binomial Edge Ideal

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 06 Oct 2017Embargo end date: 01 Jan 2016Publisher:The Electronic Journal of CombinatoricsJournal:The Electronic Journal of Combinatorics, volume 24 (eissn: 1077-8926,

Copyright policy )Publicly fundedFunded by:IRC | unidentified

Authors: Mourtadha Badiane; Isaac Burke; Emil Sköldberg;

doi: 10.37236/5912 , 10.48550/arxiv.1601.04575

arXiv: 1601.04575

The Universal Gröbner Basis of a Binomial Edge Ideal

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Abstract

We show that the universal Gröbner basis and the Graver basis of a binomial edge ideal coincide. We provide a description for this basis set in terms of certain paths in the underlying graph. We conjecture a similar result for a parity binomial edge ideal and prove this conjecture for the case when the underlying graph is the complete graph.

Related Organizations

National University of Ireland
Ireland
University of Galway
Ireland

Keywords

parity binomial edge ideals, Commutative rings defined by binomial ideals, toric rings, etc., Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), universal Gröbner basis, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Graver basis, binomial edge ideals, FOS: Mathematics, Combinatorial aspects of commutative algebra, Primary: 13P10, Secondary: 05E40

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