Additive triples of bijections, or the toroidal semiqueens problem

  • Sean Eberhard

    London, UK
  • Freddie Manners

    Stanford University, USA
  • Rudi Mrazović

    University of Zagreb, Croatia
Additive triples of bijections, or the toroidal semiqueens problem cover
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Abstract

We prove an asymptotic for the number of additive triples of bijections , that is, the number of pairs of bijections such that the pointwise sum is also a bijection. This problem is equivalent to counting the number of orthomorphisms or complete mappings of , to counting the number of arrangements of mutually nonattacking semiqueens on an toroidal chessboard, and to counting the number of transversals in a cyclic Latin square. The method of proof is a version of the Hardy–Littlewood circle method from analytic number theory, adapted to the group .

Cite this article

Sean Eberhard, Freddie Manners, Rudi Mrazović, Additive triples of bijections, or the toroidal semiqueens problem. J. Eur. Math. Soc. 21 (2019), no. 2, pp. 441–463

DOI 10.4171/JEMS/841