@techreport{RISC5164,
author = {Felix Breuer and Brandt Kronholm},
title = {{A POLYHEDRAL MODEL OF PARTITIONS WITH BOUNDED DIFFERENCES AND A BIJECTIVE PROOF OF A THEOREM OF ANDREWS, BECK, AND ROBBINS}},
language = {english},
abstract = {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 function. This result is similar to the closely related case of partitions with fixed differences between largest and smallest parts which has recently been studied through analytic methods by Andrews, Beck, and Robbins. Our approach is geometric: We model partitions with bounded differences as lattice points in an infinite union of polyhedral cones. Surprisingly, this infinite union tiles a single simplicial cone. This construction then leads to a bijection that can be interpreted on a purely combinatorial level. },
year = {2015},
month = {May},
howpublished = {arXiv },
keywords = {Integer Partitions, Polyhedral Geometry, Combinatorics, Ehrhart, Generating Function, Heine Transformation, George Andrews, Matthias Beck, Neville Robbins},
length = {12},
url = {http://arxiv.org/abs/1505.00250},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}