We prove that if $g(n; i,j)$ denotes the number of Gessel walks of length $n$ which end at the point $(i,j)\in\set N^2$, then the trivariate generating series $G(t;x,y)x^i y^j t^n$ is an algebraic function.Expand

We propose an experimental mathematics approach leading to the computer-driven discovery of various structural properties of general counting functions coming from enumeration of walks.

We prove that the sequence (e"n^S)"n">="0 of numbers of excursions in the quarter plane corresponding to a nonsingular step set S@?{0,+/-1}^2 with infinite group does not satisfy any nontrivial linear recurrence with polynomial coefficients.Expand

Le calcul formel traite des objets mathematiques exacts d’un point de vue informatique. Cet ouvrage « Algorithmes efficaces en calcul formel » explore deux directions : la calculabilite et la… Expand

We propose explicit transposed versions of polynomial multiplication and division but also new faster algorithms for multipoint evaluation, interpolation and their transposes.Expand

Linear systems with structures such as Toeplitz, Vandermonde or Cauchy-likeness can be solved in [email protected]?(@a^2n) operations, where n is the matrix size, @a is its displacement rank, and @w denotes the omission of logarithmic factors.Expand