Section: New Results

Combinatorial walks with small steps in the quarter plane

Alin Bostan and Frédéric Chyzak, together with Mark van Hoeij (Florida State University), Manuel Kauers (Johannes Kepler University), and Lucien Pech (former intern), have applied their algorithms on special functions to generate complete, quantitative results in the enumerative theory of combinatorial walks with small steps in the quarter plane [2]. They gave the first proof that differential equations conjectured years ago by Bostan and Kauers are indeed satisfied by the corresponding generating functions. They also obtained explicit hypergeometric expressions for the latter, and could provably determine which of the generating functions are transcendental or algebraic.