Analytic models and ambiguity of context-free languages
Theoretical Computer Science
A calculus for the random generation of labelled combinatorial structures
Theoretical Computer Science
Walks on the Slit Plane: Other Approaches
Advances in Applied Mathematics
Basic analytic combinatorics of directed lattice paths
Theoretical Computer Science
Walks confined in a quadrant are not always D-finite
Theoretical Computer Science - Random generation of combinatorial objects and bijective combinatorics
Partially directed paths in a wedge
Journal of Combinatorial Theory Series A
Two non-holonomic lattice walks in the quarter plane
Theoretical Computer Science
Exact tail asymptotics in a priority queue--characterizations of the preemptive model
Queueing Systems: Theory and Applications
Families of prudent self-avoiding walks
Journal of Combinatorial Theory Series A
A Representation Theorem for Holonomic Sequences Based on Counting Lattice Paths
Fundamenta Informaticae - Lattice Path Combinatorics and Applications
Non-D-finite excursions in the quarter plane
Journal of Combinatorial Theory Series A
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This work considers the nature of generating functions of random lattice walks restricted to the first quadrant. In particular, we find combinatorial criteria to decide if related series are algebraic, transcendental holonomic or otherwise. Complete results for walks taking their steps in a maximum of three directions of restricted amplitude are given, as is a well-supported conjecture for all walks with steps taken from a subset of {0,+/-1}^2. New enumerative results are presented for several classes, each obtained with a variant of the kernel method.