Proof of a conjecture on the slit plane problem

2003/04/30 by Guoce Xin
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Computational Geometry and Mesh Generation #Mathematics and Applications #math.CO #msc:05A15 #msc:60K60.66

paper · pdf · doi:10.1016/j.disc.2004.01.004

published as Discrete Mathematics, Vol 282/1-3 pp 281-287, 2004 · 7 pages

arxiv created 2004/02/11 · openalex publication_date 2004/03/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

Let a_i,j(n) denote the number of walks in n steps from (0,0) to (i,j), with steps (± 1,0) and (0,± 1), never touching a point (-k,0) with k≥ 0 after the starting point. \bous and Schaeffer conjectured a closed form for the number a_-i,i(2n) when i≥ 1. In this paper, we prove their conjecture, and give a formula for a_-i,i(2n) for i≤ -1.

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