Higher Nimbers in pawn endgames on large chessboards
Combinatorics
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0011253,
title = {Higher Nimbers in pawn endgames on large chessboards},
author = {Noam D. Elkies},
journal= {arXiv preprint arXiv:math/0011253},
year = {2007}
}
Comments
21 pages, including many chess diagrams created with the Tutelaers fonts; presented 7/2000 at the second MSRI workshop on combinatorial games