Lower bounds for contingency tables via Lorentzian polynomials

TL;DR

This paper introduces a novel lower bound for counting contingency tables, leveraging Lorentzian polynomial theory, and applies it to derive bounds on the volumes of flow and transportation polytopes, advancing combinatorial and geometric understanding.

Contribution

It provides a new lower bound for contingency tables using Lorentzian polynomials, extending prior bounds and offering insights into related polytopal volumes.

Findings

New lower bound on contingency tables

Improved bounds on flow and transportation polytope volumes

Utilizes recent Lorentzian polynomial results

Abstract

We present a new lower bound on the number of contingency tables, improving upon and extending previous lower bounds by Barvinok and Gurvits. As an application, we obtain new lower bounds on the volumes of flow and transportation polytopes. Our proofs are based on recent results on Lorentzian polynomials.