Seminar on low-dimensional mathematics
Thursday, May 6th, 2004, 16:00--17:45

Florent Hivert (Universit\'e Marne-la-Vall\'ee)
Computer aided research in combinatorics with MuPAD-Combinat

MuPAD-Combinat is a package for the computer algebra system MuPAD
2.0.0 or higher, which aims to provide an extensible toolbox for
computer exploration in algebraic combinatorics. The development
started in spring 2001 and is lead by Nicolas Thiery and myself,
together with a dozen of contributors. The package currently contains
functions to deal with usual combinatorial classes (partitions,
tableaux, decomposable classes specified by a recursive grammar, ...),
Schubert polynomials, characters of the symmetric group, and weighted
automata. It supplies the user with tools for constructing new
combinatorial classes and new algebraic objects such as combinatorial
Hopf algebras and, as an application, provides some well-known
combinatorial algebras like the algebra of symmetric functions and
various generalizations.

The goal of this talk is to present trough some research examples,
what is the help of a computer algebra system in algebraic
combinatoric. In the first part, I will draw an overview of the
functionalities of our package MuPAD-Combinat: the combinatorial
toolbox and the algebraic system. In the second part, I will try to
explain the starting point of the computations during my research on
Olshanskii-Hecke-Clifford algebra and Peaks quasi-symmetric
functions in collaboration with J.-Y. Thibon and N. Bergeron.