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

2025/08/21 by Elena Hoster, Christian Stump, Hoster, Elena +1 · 3 citations
Mathematics · #Commutative Algebra and Its Applications #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.2508.15538

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.

Citations

• Chow polynomials of uniform matroids are real-rooted
• Chow functions for partially ordered sets
• Two classes of posets with real-rooted chain polynomials
• Chain enumeration, partition lattices and polynomials with only real roots
• Real-rootedness of variations of Eulerian polynomials
• Gamma-positivity in combinatorics and geometry
• Gamma-positivity of variations of Eulerian polynomials
• Théorie Géométrique des Polynômes Eulériens

Cited by

• Chow polynomials of rank-uniform labeled posets
• Extending the ab-index
• Chow polynomials of totally nonnegative matrices and posets

Related

• Chow polynomials of rank-uniform labeled posets
• Chow polynomials of totally nonnegative matrices and posets
• Chow polynomials of uniform matroids are real-rooted
• Chow functions for partially ordered sets
• Two classes of posets with real-rooted chain polynomials