Higher nimbers in pawn endgames on large chessboards

Elkies, Noam2009-05-012002Elkies, 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.http://nrs.harvard.edu/urn-3:HUL.InstRepos:2886550We 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>k</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.en-USHigher nimbers in pawn endgames on large chessboards