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Abstract: 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 (Update)
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BibTeX entry: (Update)
Matthieu Latapy. Partitions of an integer into powers. In Discrete Mathematics and Theoretical Computer Science, Proceedings of the 1-st international conference Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG'01), pages 215--228. MIMD, July 2001. Preprint available at http://www.liafa.jussieu.fr/~latapy/. http://citeseer.ist.psu.edu/latapy01partitions.html More
@misc{ latapy01partitions,
author = "M. Latapy",
title = "Partitions of an integer into powers",
text = "Matthieu Latapy. Partitions of an integer into powers. In Discrete Mathematics
and Theoretical Computer Science, Proceedings of the 1-st international
conference Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG'01),
pages 215--228. MIMD, July 2001. Preprint available at http://www.liafa.jussieu.fr/~latapy/.",
year = "2001",
url = "citeseer.ist.psu.edu/latapy01partitions.html" }
Citations (may not include all citations):509 Introduction to Lattices and Orders (context) - Davey, Priestley - 1990
44 A Handbook of Integer Sequences (context) - Sloane - 1973
10 Chip-firing games on graphs (context) - Bjorner, Lovasz et al. - 1991
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5 Novi Comm (context) - Euler
5 Chip-firing games on directed graphs (context) - Bjorner, Lovasz - 1992
4 Odometers and systems of numeration (context) - Grabner, Liarded et al. - 1995
4 Congruence properties of the binary partition function (context) - Churchhouse - 1969
4 Binary partitions (context) - Churchhouse - 1971
4 On Mahler's partition problem (context) - Pennington - 1953
3 volume 72 of Mathematics in science and engineering (context) - Berge, Combinatorics - 1971
3 To appear in Physica D (context) - Latapy, Phan et al. - 2000
3 To appear in Theoretical Computer Science (context) - Latapy, Mantaci et al. - 1998
3 Accurate estimation of the number of binary partitions (context) - Froberg - 1977
[Article contains additional citations not shown here]
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