Higher nimbers in pawn endgames on large chessboards

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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.
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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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  • FAS Scholarly Articles [7588]
    Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University
 
 

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