Counting quadrant walks via Tutte's invariant method (extended abstract)

zbMath1440.05019arXiv1511.04298MaRDI QIDQ5111046

Olivier Bernardi, Mireille Bousquet-Mélou, Kilian Raschel

Publication date: 26 May 2020

Full work available at URL: https://arxiv.org/abs/1511.04298

zbMATH Keywords

conformal mappingsenumerationlattice walksdifferentially algebraic functions

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Enumeration in graph theory (05C30) Coloring of graphs and hypergraphs (05C15)

Related Items (12)

Walks with small steps in the 4D-orthant ⋮ Green's functions with oblique Neumann boundary conditions in the quadrant ⋮ Enumeration of three-quadrant walks via invariants: some diagonally symmetric models ⋮ Enumeration of walks with small steps avoiding a quadrant ⋮ Stochastic processes under constraints. Abstracts from the workshop held September 27 -- October 3, 2020 (hybrid meeting) ⋮ On the nature of four models of symmetric walks avoiding a quadrant ⋮ On differentially algebraic generating series for walks in the quarter plane ⋮ Asymptotics of 3-stack-sortable permutations ⋮ Counting walks with large steps in an orthant ⋮ Discrete harmonic functions in the three-quarter plane ⋮ Exact solution of some quarter plane walks with interacting boundaries ⋮ On the kernel curves associated with walks in the quarter plane

Uses Software

• Walks
• Guess.m
• LinearSystemSolver
• HalfLine
• OneDimWalks
• QuarterPlane
• WalkCarefully

Cites Work

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• Two non-holonomic lattice walks in the quarter plane
• A probabilistic method for lattice path enumeration
• Chromatic sums revisited
• On the functions counting walks with small steps in the quarter plane
• Random walks in cones
• Counting walks in a quadrant: a unified approach via boundary value problems
• Polynomial equations with one catalytic variable, algebraic series and map enumeration
• Walks in the Quarter Plane with Multiple Steps
• A human proof of Gessel’s lattice path conjecture
• Walks with small steps in the quarter plane
• Proof of Ira Gessel's lattice path conjecture
• The quasi-holonomic ansatz and restricted lattice walks
• Random Walk in a Weyl Chamber
• Counting Walks in the Quarter Plane
• The complete generating function for Gessel walks is algebraic

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