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Counting arrangements of bishops

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Combinatorial Mathematics IV

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 560))

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Abstract

The problem of the bishops is to determine the number of arrangements of n bishops on an n × n chessboard such that no bishop threatens another and every unoccupied square is threatened by at least one bishop. Two arrangements are considered equivalent if they are isomorphic by way of one of the eight symmetries of the chessboard. The total number of inequivalent solutions to the problem of the bishops is found, as well as the numbers of solutions which have each of the possible automorphism groups. The values up to n=16 are tabulated, and asymptotic formulas are found. A review of analogous results for the problem of the rooks is included, since they are made use of in studying the problem of the bishops.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Newcastle, New South Wales

    Robert W. Robinson

Authors
  1. Robert W. Robinson
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Louis R. A. Casse Walter D. Wallis

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© 1976 Springer-Verlag

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Robinson, R.W. (1976). Counting arrangements of bishops. In: Casse, L.R.A., Wallis, W.D. (eds) Combinatorial Mathematics IV. Lecture Notes in Mathematics, vol 560. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097382

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  • DOI: https://doi.org/10.1007/BFb0097382

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08053-4

  • Online ISBN: 978-3-540-37537-1

  • eBook Packages: Springer Book Archive

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