| author: | Matthieu Latapy |
|---|---|
| title: | Partitions of an Integer into Powers |
| keywords: | Integer partition, Composition, Lattice, Distributive Lattice, Discrete Dynamical Models, Chip Firing Game |
| 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. |
| If your browser does not display the abstract correctly (because of the different mathematical symbols) you may look it up in the PostScript or PDF files. | |
| reference: | Matthieu Latapy (2001), Partitions of an Integer into Powers, in Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001, Robert Cori and Jacques Mazoyer and Michel Morvan and Rémy Mosseri (eds.), Discrete Mathematics and Theoretical Computer Science Proceedings AA, pp. 215-228 |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
| ps.gz-source: | dmAA0116.ps.gz (311 K) |
| ps-source: | dmAA0116.ps (1680 K) |
| pdf-source: | dmAA0116.pdf (560 K) |
The first source gives you the `gzipped' PostScript, the second the plain PostScript and the third the format for the Adobe accrobat reader. Depending on the installation of your web browser, at least one of these should (after some amount of time) pop up a window for you that shows the full article. If this is not the case, you should contact your system administrator to install your browser correctly.
Due to limitations of your local software, the two formats may show up differently on your screen. If eg you use xpdf to visualize pdf, some of the graphics in the file may not come across. On the other hand, pdf has a capacity of giving links to sections, bibliography and external references that will not appear with PostScript.