Mardi 26 Mai
Heure: 
14:00  17:00 
Lieu: 
Salle B107, bâtiment B, Université de Villetaneuse 
Résumé: 
Efficient Algebraic Diagonals and Walks 
Description: 
Louis Dumont The diagonal of a multivariate power series F is the univariate power series Diag F generated by the diagonal terms of F. Diagonals form an important class of power series; they occur frequently in number theory, theoretical physics and enumerative combinatorics. Westudy algorithmic questions related to diagonals in the case where F is the Taylor expansion of a bivariate rational function. It is classical that in this case Diag F is an algebraic function. We propose an algorithm that computes an annihilating polynomial forDiag F. Generically, it is its minimal polynomial and is obtained in time quasilinear in its size. We show that this minimal polynomial has an exponential size with respect to the degree of the input rational function. Throughout the talk, we use a common problemof counting certain lattice walks to illustrate the capacities and limits of our tools. 

