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.Comment: 12 pages, 5 figure
