A human proof for a generalization of Shalosh B. Ekhad's 10^n Lattice Paths Theorem
| dc.creator | Loehr, Nicholas A. | |
| dc.creator | Sagan, Bruce E. | |
| dc.creator | Warrington, Gregory S. | |
| dc.date | 2005-10-04 | |
| dc.date.accessioned | 2026-07-07T06:20:53Z | |
| dc.date.available | 2026-07-07T06:20:53Z | |
| dc.description | Consider lattice paths in Z^2 taking unit steps north (N) and east (E). Fix positive integers r,s and put an equivalence relation on points of Z^2 by letting v,w be equivalent if v - w = m (r,s) for some m in Z. Call a lattice path valid if whenever it enters a point v with an E-step, then any further points of the path in the class of v are also entered with an E-step. Loehr and Warrington conjectured that the number of valid paths from (0,0) to (nr,ns) is (r+s choose r)^n. We prove this conjecture when s = 2. | |
| dc.description | 9 pages, 6 figures | |
| dc.identifier | https://arxiv.org/abs/math/0510079 | |
| dc.identifier | http://arxiv.org/abs/math/0510079 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/95437 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15 | |
| dc.title | A human proof for a generalization of Shalosh B. Ekhad's 10^n Lattice Paths Theorem | |
| dc.type | text |