The universal Gröbner basis of a binomial edge ideal

Mourtadha Badiane; Isaac Burke; Emil Sköldberg

doi:10.37236/5912

The universal Gröbner basis of a binomial edge ideal

Mourtadha Badiane
, Isaac Burke
, Emil Sköldberg

Mathematics

University of Galway

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

8 Citations (Scopus)

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.

Original language	English
Article number	#P4.11
Journal	Electronic Journal of Combinatorics
Volume	24
Issue number	4
DOIs	https://doi.org/10.37236/5912
Publication status	Published - 6 Oct 2017

Keywords

Binomial edge ideals
Graver basis
Parity binomial edge ideals
Universal gröbner basis

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10.37236/5912

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abstract = "We show that the universal Gr{\"o}bner 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.",

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AU - Burke, Isaac

AU - Sköldberg, Emil

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N2 - 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.

AB - 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.

KW - Binomial edge ideals

KW - Graver basis

KW - Parity binomial edge ideals

KW - Universal gröbner basis

UR - https://www.scopus.com/pages/publications/85031117201

U2 - 10.37236/5912

DO - 10.37236/5912

M3 - Article

AN - SCOPUS:85031117201

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VL - 24

JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

IS - 4

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ER -

The universal Gröbner basis of a binomial edge ideal

Abstract

Keywords

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