Séminaire du 8 septembre 2008.
10h30: Walking in the Quarter Plane. Manuel Kauers,
Risc, Linz, Austria.
We consider certain lattice walks in the plane that are restricted to
the first quadrant. Some years ago, Gessel conjectured that the
univariate counting function for closed walks (excursions) is holonomic.
We will first present a proof of Gessel's conjecture found together with
Doron Zeilberger and Christoph Koutschan. In the second part of the
talk, we will present the proof of a stronger property, recently
discovered together with Alin Bostan: the full (trivariate) Gessel's
counting function (for arbitrary walks) is algebraic.
Last modified: Wed Aug 20 11:30:06 CEST 2008