36 citations · 117 across the 17 of their papers we have counts for
22 papers
polyDB: A Database for Polytopes and Related Objects
Andreas Paffenholz
polyDB is a database for discrete geometric objects. The database is accessible via web and an interface from the software package polymake. It contains various datasets from the a…
Smooth polytopes with negative Ehrhart coefficients
Federico Castillo, Fu Liu, Benjamin Nill +1
We present examples of smooth lattice polytopes in dimensions 3 and higher where each coefficient of their Ehrhart polynomials that can potentially be negative is indeed negative.…
Computing convex hulls and counting integer points with polymake
Benjamin Assarf, Ewgenij Gawrilow, Katrin Herr +4
The main purpose of this paper is to report on the state of the art of computing integer hulls and their facets as well as counting lattice points in convex polytopes. Using the po…
Existence of unimodular triangulations - positive results
Christian Haase, Andreas Paffenholz, Lindsay C. Piechnik +1
Unimodular triangulations of lattice polytopes arise in algebraic geometry, commutative algebra, integer programming and, of course, combinatorics. In this article, we review sever…
Faces of Birkhoff Polytopes
Andreas Paffenholz
The Birkhoff polytope B(n) is the convex hull of all (n x n) permutation matrices, i.e., matrices where precisely one entry in each row and column is one, and zeros at all other pl…
Finiteness of the polyhedral Q-codegree spectrum
Andreas Paffenholz
In this paper we show that the spectrum of the Q-codegree of a d-dimensional lattice polytope is finite above any positive threshold in the class of lattice polytopes with α-canoni…