On the critical exponents of generalized ballot sequences in three dimensions and large tandem walks

2021/05/25 by Michael Wallner, Wallner, Michael
Mathematics · #05A15 #05A16 #05A19 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Limits and Structures in Graph Theory #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.2105.12155

openalex publication_date 2021/05/25 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We answer some questions on the asymptotics of ballot walks raised in [Personal Journal Shalosh B Ekhad and Doron Zeilberger, Apr 5, 2021; see also arXiv:2104.01731] and prove that these models are not D-finite. This short note demonstrates how the powerful tools developed in the last decades on lattice paths in convex cones help us to answer some challenging problems that were out of reach for a long time. On the way we generalize tandem walks to the family of large tandem walks whose steps are of arbitrary length and map them bijectively to a generalization of ballot walks in three dimensions.

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