75 citations · 671 across the 41 of their papers we have counts for
10 papers · 1 filter
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}\leq \c…
Three Ehrhart Quasi-polynomials
Velleda Baldoni, Nicole Berline, Jesús A. De Loera +2
Let be a semi-rational parametric polytope, where is a real multi-parameter. We study intermediate sums of polynomial functions on ,…
Intermediate Sums on Polyhedra II: Bidegree and Poisson Formula
Velleda Baldoni, Nicole Berline, Jesús A. De Loera +2
We continue our study of intermediate sums over polyhedra, interpolating between integrals and discrete sums, which were introduced by A. Barvinok [Computing the Ehrhart quasi-poly…
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…
Intermediate Sums on Polyhedra: Computation and Real Ehrhart Theory
Velleda Baldoni, Nicole Berline, Matthias Köppe +1
We study intermediate sums, interpolating between integrals and discrete sums, which were introduced by A. Barvinok [Computing the Ehrhart quasi-polynomial of a rational simplex, M…
Challenging computations of Hilbert bases of cones associated with algebraic statistics
Winfried Bruns, Raymond Hemmecke, Bogdan Ichim +2
In this paper we present two independent computational proofs that the monoid derived from contingency tables is normal, completing the classification by Hibi a…
Ehrhart polynomials of matroid polytopes and polymatroids
Jesús A. De Loera, David C. Haws, Matthias Köppe
We investigate properties of Ehrhart polynomials for matroid polytopes, independence matroid polytopes, and polymatroids. In the first half of the paper we prove that for fixed ran…
Computing parametric rational generating functions with a primal Barvinok algorithm
Matthias Köppe, Sven Verdoolaege
Computations with Barvinok's short rational generating functions are traditionally being performed in the dual space, to avoid the combinatorial complexity of inclusion--exclusion…
Computation of Atomic Fibers of Z-Linear Maps
Elke Eisenschmidt, Raymond Hemmecke, Matthias Köppe
For given matrix , the set describes the preimage or fiber of under the -linear map , $x\mapsto…
A primal Barvinok algorithm based on irrational decompositions
Matthias Köppe
We introduce variants of Barvinok's algorithm for counting lattice points in polyhedra. The new algorithms are based on irrational signed decomposition in the primal space and the…