Enumerative combinatorics
The evolution of two stacks in bounded space and random walks in a triangle
Proceedings of the 12th symposium on Mathematical foundations of computer science 1986
Analytic models and ambiguity of context-free languages
Theoretical Computer Science
Discrete Mathematics
Handbook of theoretical computer science (vol. B): formal models and semantics
Handbook of theoretical computer science (vol. B): formal models and semantics
GFUN: a Maple package for the manipulation of generating and holonomic functions in one variable
ACM Transactions on Mathematical Software (TOMS)
The random generation of directed animals
Theoretical Computer Science
Asymptotic distributions and a multivariate Darboux method in enumeration problems
Journal of Combinatorial Theory Series A
Tiling figures of the plane with two bars
Computational Geometry: Theory and Applications
An introduction to the analysis of algorithms
An introduction to the analysis of algorithms
Reconstructing convex polyominoes from horizontal and vertical projections
Theoretical Computer Science
Asymptotic enumeration methods
Handbook of combinatorics (vol. 2)
The number of convex polyominoes reconstructible from their orthogonal projections
Proceedings of the 6th conference on Formal power series and algebraic combinatorics
Images and Preimages in Random Mappings
SIAM Journal on Discrete Mathematics
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Asymptotic properties of some underdiagonal walks generation algorithms
Theoretical Computer Science - Special issue on Caen '97
Underdiagonal lattice paths with unrestricted steps
Discrete Applied Mathematics
Random maps, coalescing saddles, singularity analysis, and airy phenomena
Random Structures & Algorithms - Special issue on analysis of algorithms dedicated to Don Knuth on the occasion of his (100)8th birthday
Reconstruction of lattice sets from their horizontal, vertical and diagonal X-rays
Discrete Mathematics
Combinatorial Enumeration
Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications)
Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications)
Walks confined in a quadrant are not always D-finite
Theoretical Computer Science - Random generation of combinatorial objects and bijective combinatorics
Counting lattice paths taking steps in infinitely many directions under special access restrictions
Theoretical Computer Science - Combinatorics of the discrete plane and tilings
Exchange relations, Dyck paths and copolymer adsorption
Discrete Applied Mathematics
Polynomial equations with one catalytic variable, algebraic series and map enumeration
Journal of Combinatorial Theory Series B
Classifying lattice walks restricted to the quarter plane
Journal of Combinatorial Theory Series A
Asymptotic enumeration of constellations and related families of maps on orientable surfaces
Combinatorics, Probability and Computing
Two non-holonomic lattice walks in the quarter plane
Theoretical Computer Science
Bijections for a class of labeled plane trees
European Journal of Combinatorics
Fast computation of special resultants
Journal of Symbolic Computation
Counting colored planar maps: Algebraicity results
Journal of Combinatorial Theory Series B
Enumeration and asymptotics of restricted compositions having the same number of parts
Discrete Applied Mathematics
A Representation Theorem for Holonomic Sequences Based on Counting Lattice Paths
Fundamenta Informaticae - Lattice Path Combinatorics and Applications
Generating Functions of Embedded Trees and Lattice Paths
Fundamenta Informaticae - Lattice Path Combinatorics and Applications
Non-D-finite excursions in the quarter plane
Journal of Combinatorial Theory Series A
European Journal of Combinatorics
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This paper develops a unified enumerative and asymptotic theory of directed two-dimensional lattice paths in half-planes and quarter-planes. The lattice paths are specified by a finite set of rules that are both time and space homogeneous, and have a privileged direction of increase. (They are then essentially one-dimensional objects.) The theory relies on a specific "kernel method" that provides an important decomposition of the algebraic generating functions involved, as well as on a generic study of singularities of an associated algebraic curve. Consequences are precise computable estimates for the number of lattice paths of a given length under various constraints (bridges, excursions, meanders) as well as a characterization of the limit laws associated to several basic parameters of paths.