Infinite orders and non-\(D\)-finite property of 3-dimensional lattice walks

zbMath1344.05013arXiv1507.03705MaRDI QIDQ311562

Qing-Hu Hou, Daniel K. Du, Rong-Hua Wang

Publication date: 13 September 2016

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.03705

zbMATH Keywords

generating functions\(D\)-finitelattice walks

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Exact enumeration problems, generating functions (05A15)

Related Items (7)

Counting quadrant walks via Tutte's invariant method ⋮ Walks with small steps in the 4D-orthant ⋮ Walks in the quarter plane: genus zero case ⋮ Lattice walks in the octant with infinite associated groups ⋮ Automated positive part extraction for lattice path generating functions in the octant ⋮ Counting walks with large steps in an orthant ⋮ 3D positive lattice walks and spherical triangles

Uses Software

• Epsilon

Cites Work

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• Non-D-finite excursions in the quarter plane
• On 3-dimensional lattice walks confined to the positive octant
• Explicit expression for the generating function counting Gessel's walks
• Two non-holonomic lattice walks in the quarter plane
• Classifying lattice walks restricted to the quarter plane
• Differentiably finite power series
• Random walks in cones
• Counting walks in a quadrant: a unified approach via boundary value problems
• Bruno Buchberger's PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal. Translation from the German
• Walks with small steps in the quarter plane
• Singularity Analysis Via the Iterated Kernel Method
• Random Walk in a Weyl Chamber
• The complete generating function for Gessel walks is algebraic

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