29 citations · 154 across the 72 of their papers we have counts for
10 papers · 2 filters
Enumerating Colorings, Tensions and Flows in Cell Complexes
Matthias Beck, Felix Breuer, Logan Godkin +1
We study quasipolynomials enumerating proper colorings, nowhere-zero tensions, and nowhere-zero flows in an arbitrary CW-complex , generalizing the chromatic, tension and flow p…
The combinatorics of interval-vector polytopes
Matthias Beck, Jessica De Silva, Gabriel Dorfsman-Hopkins +2
An \emph{interval vector} is a -vector in for which all the 1's appear consecutively, and an \emph{interval-vector polytope} is the convex hull of a set of in…
s-Lecture Hall Partitions, Self-Reciprocal Polynomials, and Gorenstein Cones
Matthias Beck, Benjamin Braun, Matthias Köppe +2
In 1997, Bousquet-Melou and Eriksson initiated the study of lecture hall partitions, a fascinating family of partitions that yield a finite version of Euler's celebrated odd/distin…
On Weak Chromatic Polynomials of Mixed Graphs
Matthias Beck, Daniel Blado, Joseph Crawford +2
A \emph{mixed graph} is a graph with directed edges, called arcs, and undirected edges. A -coloring of the vertices is proper if colors from are assigned to each v…
Lattice-point generating functions for free sums of convex sets
Matthias Beck, Pallavi Jayawant, Tyrrell B. McAllister
Let $\J$ and $\K$ be convex sets in whose affine spans intersect at a single rational point in $\J \cap \K$, and let $\J \oplus \K = \conv(\J \cup \K)$. We give formulas f…
Flows on Simplicial Complexes
Matthias Beck, Yvonne Kemper
Given a graph , the number of nowhere-zero $\ZZ_q$-flows is known to be a polynomial in . We extend the definition of nowhere-zero $\ZZ_q$-flows to simplicial comple…
Lattice Point Generating Functions and Symmetric Cones
Matthias Beck, Thomas Bliem, Benjamin Braun +1
We show that a recent identity of Beck-Gessel-Lee-Savage on the generating function of symmetrically contrained compositions of integers generalizes naturally to a family of convex…
Counting Group Valued Graph Colorings
Eric Babson, Matthias Beck
There are many variations on partition functions for graph homomorphisms or colorings. The case considered here is a counting or hard constraint problem in which the range or color…
A bivariate chromatic polynomial for signed graphs
Matthias Beck, Mela Hardin
We study Dohmen--Pönitz--Tittmann's bivariate chromatic polynomial which counts all -colorings of a graph such that adjacent vertices get different colors if…
Combinatorial Reciprocity Theorems
Matthias Beck
A common theme of enumerative combinatorics is formed by counting functions that are polynomials evaluated at positive integers. In this expository paper, we focus on four families…