Guillaume Dye a donné une série de quatre téléconférences en tant que directeur d’études invité, les lundis 8, 15, 22 et 29 juin, sur le thème « Construire la communauté des croyants. Identité transmission aux débuts l’islam ».

We prove an identity conjectured by Adin and Roichman involving the descent set of λ-unimodal cyclic permutations. These permutations appear in the character formulas for certain representations of the symmetric group and these formulas are usually proven algebraically. Here, we give a combinatorial proof for one such formula and discuss the consequences for the distribution of the descent set ...

We aim to generalize a theorem on the number of rooted spanning forests of a highly symmetric graph to the case of asymmetric graphs. We show that this can be achieved by means of an identity between the minor determinants of a Laplace matrix, for which we provide two different (combinatorial as well as algebraic) proofs in the simplest case. Furthermore, we discuss the connections to electrica...