Publications (99)
Musical Chords by the Numbers
Matthias Beck, Emily Clader
The mathematics of musical intervals and scales has been extensively studied. Vastly simplified, our ears seem to prefer intervals whose frequency ratios have small numerator and d…
MacMahon's Double Vision: Partition Diamonds Revisited
Matthias Beck, Kobe Wijesekera
Plane partition diamonds were introduced by Andrews, Paule, and Riese (2001) as part of their study of MacMahon's -operator in search for integer partition identities. More rec…
Bivariate Order Polynomials
Matthias Beck, Maryam Farahmand, Gina Karunaratne +1
Motivated by Dohmen-Pönitz-Tittmann's bivariate chromatic polynomial , which counts all -colorings of a graph such that adjacent vertices get different colors if…
Generating functions and triangulations for lecture hall cones
Matthias Beck, Benjamin Braun, Matthias Köppe +2
We investigate the arithmetic-geometric structure of the lecture hall cone \[ L_n \ := \ \left\{λ\in \mathbb{R}^n: \, 0\leq \frac{λ_1}{1}\leq \frac{λ_2}{2}\leq \frac{λ_3}{3}\le…
Signed Poset Polytopes
Matthias Beck, Max Hlavacek
Stanley introduced in 1986 the order polytope and the chain polytope for a given finite poset. These polytopes contain much information about the poset and have given rise to impor…
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…