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- Alin Bostan, Manuel Kauers
- ArXiv
- 2009

Gessel walks are lattice walks in the quarter-plane N2 which start at the origin (0, 0) ∈ N2 and consist only of steps chosen from the set {←,↙,↗,→}. We prove that if g(n; i, j) denotes the number of… (More)

- Alin Bostan, Manuel Kauers
- 2008

There is a strange phenomenon about the generating functions that count lattice walks restricted to the quarter plane: depending on the choice of the set S ⊆ {↙,←,↖, ↑,↗,→,↘, ↓} of admissible steps,… (More)

- Alin Bostan, Éric Schost
- J. Complexity
- 2005

We give complexity estimates for the problems of evaluation and interpolation on various polynomial bases. We focus on the particular cases when the sample points form an arithmetic or a geometric… (More)

- Alin Bostan, Pierrick Gaudry, Éric Schost
- SIAM J. Comput.
- 2007

We study the complexity of computing one or several terms (not necessarily consecutive) in a recurrence with polynomial coefficients. As applications, we improve the best currently known upper bounds… (More)

- Alin Bostan, Frédéric Chyzak, Bruno Salvy, Grégoire Lecerf, Éric Schost
- ISSAC
- 2007

It is classical that univariate algebraic functions satisfy linear differential equations with polynomial coefficients. Linear recurrences follow for the coefficients of their power series… (More)

- Alin Bostan, Kilian Raschel, Bruno Salvy
- J. Comb. Theory, Ser. A
- 2014

We prove that the sequence (eSn )n≥0 of excursions in the quarter plane corresponding to a nonsingular step set S ⊆ {0, ±1} with infinite group does not satisfy any nontrivial linear recurrence with… (More)

- Alin Bostan, Bruno Salvy, Éric Schost
- ArXiv
- 2008

We discuss efficient conversion algorithms for orthogonal polynomials. We describe a known conversion algorithm from an arbitrary orthogonal basis to the monomial basis, and deduce a new algorithm of… (More)

- Alin Bostan, Shaoshi Chen, Frédéric Chyzak, Ziming Li
- ISSAC
- 2010

The long-term goal initiated in this work is to obtain fast algorithms and implementations for definite integration in Almkvist and Zeilberger's framework of (differential) creative telescoping. Our… (More)

We propose algorithms for the computation of the first N terms of a vector (or a full basis) of power series solutions of a linear system of differential equations at an ordinary point, using a… (More)

- Alin Bostan, Shaoshi Chen, Frédéric Chyzak, Ziming Li, Guoce Xin
- ISSAC
- 2013

We present a new reduction algorithm that simultaneously extends Hermite's reduction for rational functions and the Hermite-like reduction for hyperexponential functions. It yields a unique additive… (More)