Matthias Beck

collaborators

4 papers

math.CO2025

Generating functions of $q$ -chromatic polynomials

Matthias Beck, Benjamin Braun, Alvaro Cornejo

Given a graph $G = (V, E)$ and a linear form $λ \in Z_{> 0}^{V}$ , Bajo et al. (2025) introduced the $q$ -chromatic polynomial $χ_{G}^{λ} (q, n) := \sum q^{\sum_{v \in V} λ_{v} c (v)}$ w…

math.CO2025

A Closer Look at Chapoton's q-Ehrhart Polynomials

Matthias Beck, Thomas Kunze

If $P$ is a lattice polytope (i.e., $P$ is the convex hull of finitely many integer points in $R^{d}$ ), Ehrhart's famous theorem (1962) asserts that the…

math.CO2024

Polyhedral geometry of refined $q, t$ -Catalan numbers

Matthias Beck, Mitsuki Hanada, Max Hlavacek +3

We study a refinement of the $q, t$ -Catalan numbers introduced by Xin and Zhang (2022, 2023) using tools from polyhedral geometry. These refined $q, t$ -Catalan numbers depend on a ve…

math.CO2024

$q$ -Chromatic polynomials

Esme Bajo, Matthias Beck, Andrés R. Vindas-Meléndez

We study a $q$ -version of the chromatic polynomial of a given graph $G = (V, E)$ , namely, \[ χ_G^λ(q,n) \ := \sum_{\substack{\text{proper colorings}\\ c\,:\,V\to[n]}} q^{ \sum_{ v \in…

Generating functions of q-chromatic polynomials

A Closer Look at Chapoton's q-Ehrhart Polynomials

Polyhedral geometry of refined q,t-Catalan numbers

q-Chromatic polynomials

Generating functions of $q$ -chromatic polynomials

Polyhedral geometry of refined $q, t$ -Catalan numbers

$q$ -Chromatic polynomials