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Proof of a Conjecture on the Slit Plane Problem | | Guoce Xin
; | | Date: |
14 Apr 2003 | | Journal: | Discrete Mathematics, Vol 282/1-3 pp 281-287, 2004 DOI: 10.1016/j.disc.2004.01.004 | | Subject: | Combinatorics MSC-class: 05A15, 60K60.66 | math.CO | | Abstract: | Let $a_{i,j}(n)$ denote the number of walks in $n$ steps from $(0,0)$ to $(i,j)$, with steps $(pm 1,0)$ and $(0,pm 1)$, never touching a point $(-k,0)$ with $kge 0$ after the starting point. ous and Schaeffer conjectured a closed form for the number $a_{-i,i}(2n)$ when $ige 1$. In this paper, we prove their conjecture, and give a formula for $a_{-i,i}(2n)$ for $ile -1$. | | Source: | arXiv, math.CO/0304178 | | Services: | Forum | Review | PDF | Favorites | |
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