On 3-Dimensional Lattice Walks Confined to the Positive Octant

A human proof of Gessel’s lattice path conjecture

(2016) A. Bostan et al.   TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY

Singularity Analysis Via the Iterated Kernel Method

(2014) STEPHEN MELCZER et al.   COMBINATORICS PROBABILITY & COMPUTING

Non-D-finite excursions in the quarter plane

(2013) Alin Bostan et al.   JOURNAL OF COMBINATORIAL THEORY SERIES A

Explicit expression for the generating function counting Gesselʼs walks

(2010) Irina Kurkova et al.   ADVANCES IN APPLIED MATHEMATICS

The complete generating function for Gessel walks is algebraic

(2010) Alin Bostan et al.   PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

Proof of Ira Gessel's lattice path conjecture

(2009) Manuel Kauers et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Two non-holonomic lattice walks in the quarter plane

(2009) Marni Mishna et al.   THEORETICAL COMPUTER SCIENCE

The quasi-holonomic ansatz and restricted lattice walks

(2008) Manuel Kauers et al.   JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS