Higher Nimbers in pawn endgames on large chessboards
نویسنده
چکیده
We answer a question posed in [Elkies 1996] by constructing a class of pawn endgames onm×n 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.
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تاریخ انتشار 2002