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- W2964199483 abstract "We prove an asymptotic for the number of additive triples of bijections ${1,dots,n}tomathbb{Z}/nmathbb{Z}$, that is, the number of pairs of bijections $pi_1,pi_2colon {1,dots,n}tomathbb{Z}/nmathbb{Z}$ such that the pointwise sum $pi_1+pi_2$ is also a bijection. This problem is equivalent to counting the number of orthomorphisms or complete mappings of $mathbb{Z}/nmathbb{Z}$, to counting the number of arrangements of $n$ mutually nonattacking semiqueens on an $ntimes n$ 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 $(mathbb{Z}/nmathbb{Z})^n$." @default.
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- W2964199483 date "2018-10-24" @default.
- W2964199483 modified "2023-10-18" @default.
- W2964199483 title "Additive triples of bijections, or the toroidal semiqueens problem" @default.
- W2964199483 doi "https://doi.org/10.4171/jems/841" @default.
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