Abstract Let α=(a, b,…) be a composition. Consider the associated poset F (α), called a
fence, whose covering relations are x 1◁ x 2◁…◁ x a+ 1▷ x a+ 2▷…▷ x a+ b+ 1◁ x a+ …

In algebraic, topological, and geometric combinatorics, inequalities among the coefficients of
combinatorial polynomials are frequently studied. Recently, a notion called the alternatingly …

We investigate arithmetic, geometric and combinatorial properties of symmetric edge
polytopes. We give a complete combinatorial description of their facets. By combining …

In this paper, we first give a sufficient condition for a sequence of polynomials to have
alternatingly increasing property, and then we present a systematic study of excedance-type …

This article provides a comprehensive exposition about inequalities that the coefficients of
Ehrhart polynomials and h-polynomials satisfy under various assumptions. We pay …

The Eulerian polynomials and derangement polynomials are two well-studied generating
functions that frequently arise in combinatorics, algebra, and geometry. When one makes an …

We provide a formula for the Ehrhart polynomial of the connected matroid of size n and rank
k with the least number of bases, also known as a minimal matroid. We prove that their …

Polynomials which afford nonnegative, real‐rooted symmetric decompositions have been
investigated recently in algebraic, enumerative and geometric combinatorics. Brändén and …

Equivariant Ehrhart theory generalizes the study of lattice point enumeration to also account
for the symmetries of a polytope under a linear group action. We present a catalogue of …

Eulerian polynomials are fundamental in combinatorics and algebra. In this paper we study
the linear transformation $\mathcal {A}:\mathbb {R}[t]\to\mathbb {R}[t] $ defined by $\mathcal …