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

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.

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