English

The universal Gr\"obner basis of a binomial edge ideal

Commutative Algebra 2020-04-08 v2

Abstract

We show that the universal Gr\"obner 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.

Keywords

Cite

@article{arxiv.1601.04575,
  title  = {The universal Gr\"obner basis of a binomial edge ideal},
  author = {Mourtadha Badiane and Isaac Burke and Emil Sköldberg},
  journal= {arXiv preprint arXiv:1601.04575},
  year   = {2020}
}

Comments

12 pages, 1 figure, v2: added introduction, updated layout, fixed several typos, added examples, standardised notation, changed references

R2 v1 2026-06-22T12:31:50.641Z