Continued Classification of 3D Lattice Walks in the Positive Octant

zbMath1440.05017arXiv1511.05763MaRDI QIDQ5110946

Manuel Kauers, Rika Yatchak, Axel Bacher

Publication date: 26 May 2020

Full work available at URL: https://arxiv.org/abs/1511.05763

zbMATH Keywords

asymptoticscomputer algebralattice walksD-finiteness

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Exact enumeration problems, generating functions (05A15) Computational methods for problems pertaining to combinatorics (05-08)

Related Items (6)

Walks with small steps in the 4D-orthant ⋮ Non-D-finite walks in a three-quadrant cone ⋮ Lattice walks in the octant with infinite associated groups ⋮ Computation of Tight Enclosures for Laplacian Eigenvalues ⋮ 3D positive lattice walks and spherical triangles ⋮ Inhomogeneous restricted lattice walks

Uses Software

• GAP
• SageMath

Cites Work

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• Non-D-finite excursions in the quarter plane
• On 3-dimensional lattice walks confined to the positive octant
• On the exit time from a cone for random walks with drift
• 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
• Basic analytic combinatorics of directed lattice paths
• On the functions counting walks with small steps in the quarter plane
• A combinatorial understanding of lattice path asymptotics
• Counting walks in a quadrant: a unified approach via boundary value problems
• 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
• Automatic Classification of Restricted Lattice Walks
• The complete generating function for Gessel walks is algebraic

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