author: | Nicolas M. Thiéry |
---|---|

title: | Computing Minimal Generating Sets of Invariant Rings of Permutation Groups with SAGB I-Gröbner Basis |

keywords: | Invariant Theory, Permutation Group, Discrete Mathematics, Minimal Generating Set, Hironaka Decomposition, SAGBI-Gröbner basis, permuvar, mupad |

abstract: | We present a characteristic-free algorithm for computing minimal generating sets of invariant rings of permutation groups. We circumvent the main weaknesses of the usual approaches (using classical Gröbner basis inside the full polynomial ring, or pure linear algebra inside the invariant ring) by relying on the theory of SAGBI-Gröbner basis. This theory takes, in this special case, a strongly combinatorial flavor, which makes it particularly effective. Our algorithm does not require the computation of a Hironaka decomposition, nor even the computation of a system of parameters, and could be parallelized. Our implementation, as part of the library permuvar for mupad, is in many cases much more efficient than the other existing software. |

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: | Nicolas M. Thiéry
(2001), Computing Minimal Generating Sets of Invariant Rings
of Permutation Groups with
SAGB
I-Gröbner Basis, 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.
315-328 |

bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |

ps.gz-source: | dmAA0123.ps.gz (46 K) |

ps-source: | dmAA0123.ps (130 K) |

pdf-source: | dmAA0123.pdf (131 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.

Automatically produced on Di Sep 27 10:09:07 CEST 2005 by gustedt