Directed lattice paths avoiding periodic subset of points on "time"-axis

2025/10/13 by Tarasov, S.
#05A1 #05A10 #05A15 #Combinatorics (math.CO) #FOS: Mathematics #G.2

paper · doi:10.48550/arxiv.2510.11367

Abstract

We compute generating functions of the set of directed lattice paths starting from the origin and avoiding a periodic set of even point on OX = "time"-axis. As an application we prove a combinatorial identity proposed by P. Hajnal and G.V. Nagy.

Citations

• On the Asymptotics and the Non-Holonomic Character of First Returns in the Standard Euclidean Lattice
• Polya's random walk theorem

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• Generating functions of lattice paths
• Simple formulas for lattice paths avoiding certain periodic staircase boundaries
• Analytic Combinatorics of Planar Lattice Paths
• Generating functions for a lattice path model introduced by Deutsch
• A short conceptual proof of Narayana's path-counting formula