Matthias Beck

activity

20012026

most citedMaximal Periods of (Ehrhart) Quasi-Polynomials

29 citations · 154 across the 72 of their papers we have counts for

collaborators

85 papers

math.CO2026

Lonely Runner Relations

Matthias Beck, Samuel Everett

We study the Lonely Runner Conjecture (LRC), conceived by Jörg M. Wills in the 1960's: Given positive integers $n_{1}, n_{2}, \dots, n_{k}$ , there exists a positive real number $t$ such…

math.CO2026

Bergeron's conjecture & a tale of two binomial coefficients

Tewodros Amdeberhan, Matthias Beck

Bergeron's conjecture states that, if $1 \leq a < b < c < d$ are integers with $a d = b c$ , then one has the coefficient-wise inequality $(b b + c)_{q} \geq (a a + d)_{q}$ among two Gaus…

math.MG2023

Deep lattice points in zonotopes, lonely runners, and lonely rabbits

Matthias Beck, Matthias Schymura

Let $K \subseteq R^{d}$ be a convex body and let $w \in int (K)$ be an interior point of $K$ . The coefficient of asymmetry $\operatorname{ca}(K,\mathb…

math.CO2022

Boundary $h^{*}$ -polynomials of rational polytopes

Esme Bajo, Matthias Beck

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

math.CO2022

Lattice zonotopes of degree 2

Matthias Beck, Ellinor Janssen, Katharina Jochemko

The Ehrhart polynomial $e h r_{P} (n)$ of a lattice polytope $P$ gives the number of integer lattice points in the $n$ -th dilate of $P$ for all integers $n \geq 0$ . The degree of $P$ is…

math.CO2021

Bivariate Chromatic Polynomials of Mixed Graphs

Matthias Beck, Sampada Kolhatkar

The bivariate chromatic polynomial $χ_{G} (x, y)$ of a graph $G = (V, E)$ , introduced by Dohmen-Pönitz-Tittmann (2003), counts all $x$ -colorings of $G$ such that adjacent vertices get…