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

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.