Orateur
Mireille Bousquet-Mélou
(LaBRI, U. Bordeaux)
Description
Some families of combinatorial objects, on which a cyclic group G acts, exhibit a "cyclic sieving phenomenon": this means that for any size n, there exists a nice polynomial P(q), with integer coefficients, such that the value of P at any primitive d-th root of unity gives... the number of objects of size n that are fixed by any element of G of order d. Strange! In particular, P(1) is the total number of objects of size n. We will show such phenomena for various actions of a cyclic group on families plane trees (this is joint work with Christian Krattenthaler, from Vienna) and on plane maps (this is joint work with Marie Albenque, from Paris).