Higher Nimbers in pawn endgames on large chessboards

dc.creatorElkies, Noam D.
dc.date2000-11-29
dc.date.accessioned2026-07-07T04:38:55Z
dc.date.available2026-07-07T04:38:55Z
dc.descriptionWe 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.description21 pages, including many chess diagrams created with the Tutelaers fonts; presented 7/2000 at the second MSRI workshop on combinatorial games
dc.identifierhttps://arxiv.org/abs/math/0011253
dc.identifierhttp://arxiv.org/abs/math/0011253
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60469
dc.subjectCombinatorics
dc.titleHigher Nimbers in pawn endgames on large chessboards
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