100 citations · 291 across the 51 of their papers we have counts for
17 papers · 1 filter
Polytope volume in Normaliz
Winfried Bruns
We survey the computation of polytope volumes by the algorithms of Normaliz to which the Lawrence algorithm has recently been added. It has enabled us to master volume computations…
Automorphism groups and normal forms in Normaliz
Winfried Bruns
We discuss the computation of automorphism groups and normal forms of cones and polyhedra in Normaliz, and indicate its implementation via nauty. The types of automorphisms include…
Computations of volumes in five candidates elections
Winfried Bruns, Bogdan Ichim
We describe several analytical results obtained in five candidates social choice elections under the assumption of the Impartial Anonymous Culture. These include the Condorcet and…
Algebraic polytopes in Normaliz
Winfried Bruns
We describe the implementation of algebraic polyhedra in Normaliz. In addition to convex hull computation/vertex enumeration, it is possible to compute triangulations, volumes, lat…
Wilf's conjecture in fixed multiplicity
Winfried Bruns, Pedro Garcia-Sanchez, Christopher O'Neill +1
We give an algorithm to determine whether Wilf's conjecture holds for all numerical semigroups with a given multiplicity , and use it to prove Wilf's conjecture holds whenever $…
The monoid of monotone functions on a poset and quasi-arithmetic multiplicities for uniform matroids
Winfried Bruns, Pedro A. García-Sánchez, Luca Moci
We describe the structure of the monoid of natural-valued monotone functions on an arbitrary poset. For this monoid we provide a presentation, a characterization of prime elements,…
Computations of volumes and Ehrhart series in four candidates elections
Winfried Bruns, Bogdan Ichim, Christof Söger
We describe several experimental results obtained in four candidates social choice elections. These include the Condorcet and Borda paradoxes, as well as the Condorcet efficiency o…
Normaliz 2013-2016
Winfried Bruns, Richard Sieg, Christof Söger
In this article we describe mathematically relevant extensions to Normaliz that were added to it during the support by the DFG SPP "Algorithmische und Experimentelle Methoden in Al…
The subdivision of large simplicial cones in Normaliz
Winfried Bruns, Richard Sieg, Christof Söger
Normaliz is an open-source software for the computation of lattice points in rational polyhedra, or, in a different language, the solutions of linear diophantine systems. The two m…
Unimodular triangulations of simplicial cones by short vectors
Michael von Thaden, Winfried Bruns
We establish a bound for the length of vectors involved in a unimodular triangulation of simplicial cones. The bound is exponential in the square of the logarithm of the multiplici…
Quantum jumps of normal polytopes
Winfried Bruns, Joseph Gubeladze, Mateusz Michałek
We introduce a partial order on the set of all normal polytopes in R^d. This poset NPol(d) is a natural discrete counterpart of the continuum of convex compact sets in R^d, ordered…
Binomial regular sequences and free sums
Winfried Bruns
Recently several authors have proved results on Ehrhart series of free sums of rational polytopes. In this note we treat these results from an algebraic viewpoint. Instead of attac…
The computation of generalized Ehrhart series in Normaliz
Winfried Bruns, Christof Söger
We describe an algorithm for the computation of generalized (or weighted) Ehrhart series based on Stanley decompositions as implemented in the offspring NmzIntegrate of Normaliz. T…
The power of pyramid decomposition in Normaliz
Winfried Bruns, Bogdan Ichim, Christof Söger
We describe the use of pyramid decomposition in Normaliz, a software tool for the computation of Hilbert bases and enumerative data of rational cones and affine monoids. Pyramid de…
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…
On the integral Caratheodory property
Winfried Bruns
In this note we document the existence of a finitely generated rational cone that is not covered by its unimodular Hilbert subcones, but satisfies the integral Caratheodory propert…
Unimodular covers of multiples of polytopes
Winfried Bruns, Joseph Gubeladze
Let P be a d-dimensional lattice polytope. We show that there exists a natural number c_d, only depending on d, such that the multiples cP have a unimodular cover for every natural…