Higher nimbers in pawn endgames on large chessboards

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Title:	Higher nimbers in pawn endgames on large chessboards
Author:	Elkies, Noam
Citation:	Elkies, Noam D. 2002. Higher nimbers in pawn endgames on large chessboards. In More Games of No Chance 42, ed. Richard J. Nowakowski, 61-78. Cambridge: Cambridge University Press.
Full Text & Related Files:	Elkies - Higher Nimbers in pawn endgames.pdf (198.6Kb; PDF)
Abstract:	We answer a question posed in [Elkies 1996] by constructing a class of pawn endgames on mXn boards that show the Nimbers k for many large k. We do this by modifying and generalizing T.R. Dawson’s “pawns game” [Berlekamp et al. 1982]. Our construction works for m ≥ 9 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.
Published Version:	http://www.msri.org/communications/books/Book42/contents.html
Other Sources:	http://arxiv.org/abs/math/0011253
Terms of Use:	This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA
Citable link to this page:	http://nrs.harvard.edu/urn-3:HUL.InstRepos:2886550

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