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 quasi-linear 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.