31 citations · 57 across the 15 of their papers we have counts for
17 papers
The Arboricity Polynomial
Felix Breuer, Caroline J Klivans
We introduce a new matroid (graph) invariant, the arboricity polynomial. Given a matroid, the arboricity polynomial enumerates the number of covers of the ground set by disjoint in…
Polyhedral geometry, supercranks, and combinatorial witnesses of congruences for partitions into three parts
Felix Breuer, Dennis Eichhorn, Brandt Kronholm
In this paper, we use a branch of polyhedral geometry, Ehrhart theory, to expand our combinatorial understanding of congruences for partition functions. Ehrhart theory allows us to…
A polyhedral model of partitions with bounded differences and a bijective proof of a theorem of Andrews, Beck, and Robbins
Felix Breuer, Brandt Kronholm
The main result of this paper is a bijective proof showing that the generating function for partitions with bounded differences between largest and smallest part is a rational func…
Polyhedral Omega: A New Algorithm for Solving Linear Diophantine Systems
Felix Breuer, Zafeirakis Zafeirakopoulos
Polyhedral Omega is a new algorithm for solving linear Diophantine systems (LDS), i.e., for computing a multivariate rational function representation of the set of all non-negative…
An Invitation to Ehrhart Theory: Polyhedral Geometry and its Applications in Enumerative Combinatorics
Felix Breuer
In this expository article we give an introduction to Ehrhart theory, i.e., the theory of integer points in polyhedra, and take a tour through its applications in enumerative combi…
Scheduling Problems
Felix Breuer, Caroline J. Klivans
We introduce the notion of a scheduling problem which is a boolean function over atomic formulas of the form . Considering the as jobs to be performed, an i…