Identically distributed pairs of partition statistics.
Infinite products over hyperpyramid lattices.
Integer partitions and convexity.
Integer partitions into arithmetic progressions with an odd common difference.
Integer partitions, tilings of -gons and lattices
In this paper, we study two kinds of combinatorial objects, generalized integer partitions and tilings of -gons (hexagons, octagons, decagons, etc.). We show that the sets of partitions, ordered with a simple dynamics, have the distributive lattice structure. Likewise, we show that the set of tilings of a -gon is the disjoint union of distributive lattices which we describe. We also discuss the special case of linear integer partitions, for which other dynamical models exist.
Integer Partitions, Tilings of 2D-gons and Lattices
In this paper, we study two kinds of combinatorial objects, generalized integer partitions and tilings of 2D-gons (hexagons, octagons, decagons, etc.). We show that the sets of partitions, ordered with a simple dynamics, have the distributive lattice structure. Likewise, we show that the set of tilings of a 2D-gon is the disjoint union of distributive lattices which we describe. We also discuss the special case of linear integer partitions, for which other dynamical models exist.
Integer partitions with fixed subsums.