#### Vol. 11, No. 2, 2020

 Recent Issues Volume 11, Issue 2 Volume 11, Issue 1
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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 ${x}_{i}$, and write ${I}_{B}$ for the ideal generated by these binomials. We define a new measure of the complexity of the saturation of the ideal ${I}_{B}$ with respect to the product of the ${x}_{i}$, 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