The quasi-holonomic ansatz and restricted lattice walks

DOI10.1080/10236190802332084zbMath1193.05014arXiv0806.4318OpenAlexW2964180469MaRDI QIDQ3534870

Doron Zeilberger, Manuel Kauers

Publication date: 5 November 2008

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0806.4318

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15)

Related Items (8)

An elementary solution of Gessel's walks in the quadrant ⋮ Percolation on Triangulations: A Bijective Path to Liouville Quantum Gravity ⋮ On 3-dimensional lattice walks confined to the positive octant ⋮ Counting quadrant walks via Tutte's invariant method (extended abstract) ⋮ Proof of Ira Gessel's lattice path conjecture ⋮ Classifying lattice walks restricted to the quarter plane ⋮ Square lattice walks avoiding a quadrant ⋮ A human proof of Gessel’s lattice path conjecture

Uses Software

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

Cites Work

• Walks in the quarter plane: Kreweras' algebraic model
• The method of differentiating under the integral sign
• An algorithmic proof theory for hypergeometric (ordinary and ``\(q\)) multisum/integral identities
• Multi-variable Zeilberger and Almkvist-Zeilberger algorithms and the sharpening of Wilf-Zeilberger theory
• A probabilistic method for lattice path enumeration
• A holonomic systems approach to special functions identities
• Walks confined in a quadrant are not always D-finite
• The holonomic ansatz. I: Foundations and applications to lattice path counting

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