Partitions of an Integer into Powers

Matthieu Latapy (1)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

In this paper, we use a simple discrete dynamical model to study partitions of integers into powers of another integer. We extend and generalize some known results about their enumeration and counting, and we give new structural results. In particular, we show that the set of these partitions can be ordered in a natural way which gives the distributive lattice structure to this set. We also give a tree structure which allow efficient and simple enumeration of the partitions of an integer.

Mots clés: Integer partition; Composition; Lattice; Distributive Lattice; Discrete Dynamical Models; Chip Firing Game

Domaines: Informatique [cs]; Mathématique discrète [cs.DM]; Géométrie algorithmique [cs.CG]; Combinatoire [math.CO]

Matthieu Latapy. Partitions of an Integer into Powers. Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001, 2001, Paris, France. pp.215-228, ⟨10.46298/dmtcs.2279⟩. ⟨hal-01182959⟩