Publication: Higher nimbers in pawn endgames on large chessboards
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Date
2002
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Cambridge University Press
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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 <i>*k</i> for many large <k>k</k>. We do this by modifying and generalizing T.R. Dawson’s “pawns game” [Berlekamp et al. 1982]. Our construction works for <i>m</i> ≥ 9 and <i>n</i> sufficiently large; on the basis of computational evidence we conjecture, but cannot yet prove, that the construction yields <i>*k</i> for all integers <i>k</i>.
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