Higher Nimbers in pawn endgames on large chessboards
| dc.creator | Elkies, Noam D. | |
| dc.date | 2000-11-29 | |
| dc.date.accessioned | 2026-07-07T04:38:55Z | |
| dc.date.available | 2026-07-07T04:38:55Z | |
| dc.description | We answer a question posed in [Elkies 1996] (math.CO/9905198) by constructing a class of pawn endgames on m-by-n boards that show the Nimbers *k for large k. We do this by modifying and generalizing T.R. Dawson's ``pawns game'' [Berlekamp et al. 1982] (Winning Ways I). Our construction works for m>8 and n sufficiently large; on the basis of computational evidence we conjecture, but cannot yet prove, that the construction yields *k for all integers k. | |
| dc.description | 21 pages, including many chess diagrams created with the Tutelaers fonts; presented 7/2000 at the second MSRI workshop on combinatorial games | |
| dc.identifier | https://arxiv.org/abs/math/0011253 | |
| dc.identifier | http://arxiv.org/abs/math/0011253 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60469 | |
| dc.subject | Combinatorics | |
| dc.title | Higher Nimbers in pawn endgames on large chessboards | |
| dc.type | text |