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

## TL;DR

This paper introduces a new measure called the norm to quantify the complexity of saturations of binomial ideals, providing bounds and exploring applications in statistics.

## Contribution

It defines the norm of the saturation of binomial ideals and establishes bounds based on computable invariants, with applications to statistical models.

## Key findings

- Bound on the norm in terms of ideal invariants
- Application to statistical models and Markov bases
- New measure for ideal saturation complexity

## Abstract

Given a pure binomial ideal I in variables x_i, we define a new measure of the complexity of the saturation of I with respect to the product of the variables x_i, which we call the norm. We give a bound on the norm in terms of easily-computed invariants of the ideal. We discuss statistical applications both practical and theoretical.