Lattice point enumeration of polytopes associated to integer compositions

2025/10/27 by Athanasiadis, Christos A.
#52B20 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.23903

Abstract

An n-dimensional lattice polytope \mathcal Q_σ can be associated to any composition σ of a positive integer n, as a special case of constructions due to Pitman--Stanley and Chapoton. The entries of the h-vector of σ, introduced by Chapoton, enumerate the lattice points in \mathcal Q_σ by the number of their zero coordinates. Chapoton conjectured that this vector is equal to the h-vector of a simplicial polytope. This paper proves that the h-vector of σ is gamma-positive, hence palindromic and unimodal, and confirms certain other conjectures of Chapoton on the lattice point enumeration of composition polytopes. A combinatorial interpretation of their h^∗-polynomials is deduced.

Citations

• On posets and polytopes attached to arbors
• Rook matroids and log-concavity of P-Eulerian polynomials
• Two classes of posets with real-rooted chain polynomials
• Gamma-positivity in combinatorics and geometry
• Poset Topology: Tools and Applications
• A polytope related to empirical distributions, plane trees, parking functions, and the associahedron

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