On the nature of four models of symmetric walks avoiding a quadrant

DOI10.1007/s00026-021-00541-8zbMath1472.05006arXiv2006.02299OpenAlexW3033946084MaRDI QIDQ1980998

Publication date: 9 September 2021

Published in: Annals of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.02299

zbMATH Keywords

transcendence elliptic functions difference Galois theory random walks in the three quarter plane

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Linear difference equations (39A06)

Related Items (2)

Enumeration of three-quadrant walks via invariants: some diagonally symmetric models ⋮ Enumeration of walks with small steps avoiding a quadrant

Cites Work

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Asymptotic lattice path enumeration using diagonals
Explicit expression for the generating function counting Gessel's walks
Hypergeometric expressions for generating functions of walks with small steps in the quarter plane
Square lattice walks avoiding a quadrant
Two non-holonomic lattice walks in the quarter plane
New steps in walks with small steps in the quarter plane: series expressions for the generating functions
Differential Galois theory of linear difference equations
Basic analytic combinatorics of directed lattice paths
On the nature of the generating series of walks in the quarter plane
On the functions counting walks with small steps in the quarter plane
Counting walks with large steps in an orthant
Walks in the quarter plane: genus zero case
Winding of simple walks on the square lattice
On walks avoiding a quadrant
Random walks in cones
Non-D-finite walks in a three-quadrant cone
Counting walks in a quadrant: a unified approach via boundary value problems
Walks in the Quarter Plane with Multiple Steps
Random walks in the quarter plane with zero drift: an explicit criterion for the finiteness of the associated group
Some exact asymptotics in the counting of walks in the quarter-plane
Walks with small steps in the quarter plane
On the Holonomy or Algebraicity of Generating Functions Counting Lattice Walks in the Quarter-Plane
Singularity Analysis Via the Iterated Kernel Method
The complete generating function for Gessel walks is algebraic
Asymptotics of lattice walks via analytic combinatorics in several variables
Counting quadrant walks via Tutte's invariant method (extended abstract)
Differential transcendence & algebraicity criteria for the series counting weighted quadrant walks

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