Partitions of an Integer into Powers

Abstract : 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.
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Cori, Robert and Mazoyer, Jacques and Morvan, Michel and Mosseri, Rémy. Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001, 2001, Paris, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001), pp.215-228, 2001, DMTCS Proceedings
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Matthieu Latapy. Partitions of an Integer into Powers. Cori, Robert and Mazoyer, Jacques and Morvan, Michel and Mosseri, Rémy. Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001, 2001, Paris, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001), pp.215-228, 2001, DMTCS Proceedings. 〈hal-01182959〉

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