The number of lattice paths below a cyclically shifting boundary

2007/12/19 by J. Irving, Irving, J., Amarpreet Rattan +2 · 1 citation
Mathematics · #05A15 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #math.CO #msc:05A15

paper · pdf · doi:10.48550/arxiv.0712.3213

20 pages, 13 figures

arxiv created 2007/12/19 · openalex publication_date 2007/12/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We count the number of lattice paths lying under a cyclically shifting piecewise linear boundary of varying slope. Our main result extends well known enumerative formulae concerning lattice paths, and its derivation involves a classical reflection argument. A refinement allows for the counting of paths with a specified number of corners. We also apply the result to examine paths dominated by periodic boundaries.

Citations

• Combinatorial Enumeration

Cited by

• Polynomial Coefficient Enumeration

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