Walks obeying two-step rules on the square lattice: full, half and quarter planes

DOI10.37236/10007zbMath1481.05009arXiv2010.06955OpenAlexW3092673222MaRDI QIDQ2073308

Nicholas R. Beaton

Publication date: 1 February 2022

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

Full work available at URL: https://arxiv.org/abs/2010.06955

zbMATH Keywords

lattice walkssmall steps modeltwo-step rules

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Asymptotic enumeration (05A16)

Related Items (2)

Enumeration of corner polyhedra and 3-connected Schnyder labelings ⋮ Enumeration of corner polyhedra and 3-connected Schnyder labelings

Uses Software

• SageMath
• GitHub

Cites Work

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• An elementary solution of Gessel's walks in the quadrant
• Wielandt's proof of the exponent inequality for primitive nonnegative matrices
• Two non-holonomic lattice walks in the quarter plane
• Basic analytic combinatorics of directed lattice paths
• The kernel method: a collection of examples
• Walks confined in a quadrant are not always D-finite
• On the functions counting walks with small steps in the quarter plane
• Unzerlegbare, nicht negative Matrizen
• Ore Polynomials in Sage
• 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
• On anisotropic spiral self-avoiding walks
• On the symmetry classes of planar self-avoiding walks
• The complete generating function for Gessel walks is algebraic

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