Vol. 11, No. 2, 2020

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The norm of the saturation of a binomial ideal, with applications to Markov bases

David Holmes

Vol. 11 (2020), No. 2, 169–187
Abstract

Let B be a finite set of pure binomials in the variables xi, and write IB for the ideal generated by these binomials. We define a new measure of the complexity of the saturation of the ideal IB with respect to the product of the xi, which we call the norm of B. We give a bound on the norm in terms of easily computed invariants of B. We discuss statistical applications, both practical and theoretical.

Keywords
markov basis, saturation, toric ideals
Mathematical Subject Classification 2010
Primary: 13P25, 14M25
Milestones
Received: 17 September 2019
Revised: 26 May 2020
Accepted: 6 July 2020
Published: 28 December 2020
Authors
David Holmes
Mathematisch Instituut Leiden
Niels Bohrweg 1
2333 CA Leiden
Netherlands