Abstract
Enumeration of planar lattice walks is a classical topic in combinatorics, at the cross-roads of several domains (e.g., probability, statistical physics, computer science). The aim of this paper is to propose a new approach to obtain some exact asymptotics for walks confined to the quarter plane.
Highlights
Enumeration of planar lattice walks is a most classical topic in combinatorics
What is the asymptotic behavior, as their length goes to infinity, of the number of walks ending at some given point or domain?
What is the nature of the generating function of the numbers of walks? Is it holonomic(i), and, in that case, algebraic or even rational?
Summary
Enumeration of planar lattice walks is a most classical topic in combinatorics. For a given set S of admissible steps (or jumps), it is a matter of counting the number of paths of a certain length, which start and end at some arbitrary points, and might even be restricted to some region of the plane.
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