Chow polynomials of simplicial posets with positive $h$-vector are real-rooted

TL;DR

This paper proves that certain graded simplicial posets with positive h-vectors have real-rooted Chow polynomials, extending to Cohen-Macaulay posets and lattices of flats of uniform matroids.

Contribution

It establishes the real-rootedness of Chow and augmented Chow polynomials for a broad class of simplicial posets with positive h-vectors, including Cohen-Macaulay cases.

Findings

Chow polynomials are real-rooted for these posets.

Includes lattices of flats of uniform matroids as special cases.

Extends previous results to a wider class of posets.

Abstract

We prove that a finite graded simplicial poset with a top element added has real-rooted Chow and augmented Chow polynomials whenever it has a positive $h$-vector. This class of posets include Cohen-Macaulay simplicial posets and in particular lattices of flats of uniform matroids.