An algebraic-combinatorial proof of a Bezout-type inequality for mixed volumes of three-dimensional zonoids

TL;DR

This paper introduces an algebraic-combinatorial proof for a Bezout-type inequality involving mixed volumes of three-dimensional zonoids, revealing new connections with real algebra and matroid theory.

Contribution

It provides a novel algebraic-combinatorial proof of a known inequality, linking mixed volume inequalities with algebra and matroid theory.

Findings

New algebraic-combinatorial proof of the inequality

Connections between mixed volume inequalities and matroid theory

Potential implications for real algebra and convex geometry

Abstract

We present a new algebraic-combinatorial approach to proving a Bezout-type inequality for zonoids in dimension three, which has recently been established by Fradelizi, Madiman, Meyer, and Zvavitch. Our approach hints at connections between inequalities for mixed volumes of zonoids and real algebra and matroid theory.