29 citations · 154 across the 72 of their papers we have counts for
7 papers · 1 filter
Cyclotomic Polytopes and Growth Series of Cyclotomic Lattices
Matthias Beck, Serkan Hosten
The coordination sequence of a lattice encodes the word-length function with respect to , a set that generates as a monoid. We investigate the coordination sequence of t…
Theorems of Brion, Lawrence, and Varchenko on rational generating functions for cones
Matthias Beck, Christian Haase, Frank Sottile
We discuss and give elementary proofs of results of Brion and of Lawrence-Varchenko on the lattice-point enumerator generating functions for polytopes and cones. This largely expos…
An Enumerative Geometry for Magic and Magilatin Labellings
Matthias Beck, Thomas Zaslavsky
A magic labelling of a set system is a labelling of its points by distinct positive integers so that every set of the system has the same sum, the magic sum. Examples are magic squ…
Ehrhart-Macdonald reciprocity extended
Matthias Beck, Richard Ehrenborg
For a convex polytope P with rational vertices, we count the number of integer points in integral dilates of P and its interior. The Ehrhart-Macdonald reciprocity law gives an inti…
Volume computation for polytopes and partition functions for classical root systems
M. Welleda Baldoni, Matthias Beck, Charles Cochet +1
This paper presents an algorithm to compute the value of the inverse Laplace transforms of rational functions with poles on arrangements of hyperplanes. As an application, we prese…
Determinations of Analogues of Gauss Sums and Other Trigonometric Sums
Matthias Beck, Bruce C. Berndt, O-Yeat Chan +1
Explicit determinations of several classes of trigonometric sums are given. These sums can be viewed as analogues or generalizations of Gauss sums. In a previous paper, two of the…
Irrational proofs for three theorems of Stanley
Matthias Beck, Frank Sottile
We give new proofs of three theorems of Stanley on generating functions for the integer points in rational cones. The first, Stanley's reciprocity theorem, relates the rational gen…