Proof of a Conjecture on the Slit Plane Problem
| dc.creator | Xin, Guoce | |
| dc.date | 2003-04-14 | |
| dc.date | 2004-02-11 | |
| dc.date.accessioned | 2026-07-07T04:56:51Z | |
| dc.date.available | 2026-07-07T04:56:51Z | |
| dc.description | 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 $k\ge 0$ after the starting point. \bous and Schaeffer conjectured a closed form for the number $a_{-i,i}(2n)$ when $i\ge 1$. In this paper, we prove their conjecture, and give a formula for $a_{-i,i}(2n)$ for $i\le -1$. | |
| dc.description | 7 pages | |
| dc.identifier | https://arxiv.org/abs/math/0304178 | |
| dc.identifier | http://arxiv.org/abs/math/0304178 | |
| dc.identifier | Discrete Mathematics, Vol 282/1-3 pp 281-287, 2004 | |
| dc.identifier | doi:10.1016/j.disc.2004.01.004 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67070 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15, 60K60.66 | |
| dc.title | Proof of a Conjecture on the Slit Plane Problem | |
| dc.type | text |