Higher Nimbers in pawn endgames on large chessboards

Details Higher Nimbers in pawn endgames on large chessboards Higher Nimbers in pawn endgames on large chessboards

2000-11-29

arxiv.org/abs/math/0011253v1

Mathematics

Combinatorics

21 pages, including many chess diagrams created with the Tutelaers fonts; presented 7/2000 at the second MSRI workshop on comb

Scientific paper

We answer a question posed in [Elkies 1996] (math.CO/9905198) by constructing a class of pawn endgames on m-by-n boards that show the Nimbers *k for large k. We do this by modifying and generalizing T.R. Dawson's ``pawns game'' [Berlekamp et al. 1982] (Winning Ways I). Our construction works for m>8 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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