Matthias Beck

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20012026

most citedMaximal Periods of (Ehrhart) Quasi-Polynomials

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

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63 papers · 1 filter

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.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…

math.CO2021

Rational Ehrhart Theory

Matthias Beck, Sophia Elia, Sophie Rehberg

The Ehrhart quasipolynomial of a rational polytope $P$ encodes fundamental arithmetic data of $P$ , namely, the number of integer lattice points in positive integr…