Enumerating path diagrams in connection with q-tangent and q-secant numbers

2019/07/09 by Anum Khalid, Khalid, Anum, Thomas Prellberg +1
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Random Matrices and Applications #math.CO

paper · pdf · doi:10.48550/arxiv.1907.04172

25 pages, 1 figure

arxiv created 2019/07/09 · openalex publication_date 2019/07/09 · arxiv updated 2019/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We enumerate height-restricted path diagrams associated with q-tangent and q-secant numbers by considering convergents of continued fractions, leading to expressions involving basic hypergeometric functions. Our work generalises some results by M. Josuat-Vergés for unrestricted path diagrams [European Journal of Combinatorics 31 (2010) 1892].

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