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Additive latin transversals

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Abstract

We prove that for every odd primep, everyk≤p and every two subsets A={a 1, …,a k } andB={b 1, …,b k } of cardinalityk each ofZ p , there is a permutationπ ∈S k such that the sumsa i +b π(i) (inZ p ) are pairwise distinct. This partially settles a question of Snevily. The proof is algebraic, and implies several related results as well.

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Authors and Affiliations

  1. Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Tel Aviv, Israel

    Noga Alon

  2. Institute for Advanced Study, 08540, Princeton, NJ, USA

    Noga Alon

Authors
  1. Noga Alon
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Correspondence to Noga Alon.

Additional information

Research supported in part by a State of New Jersey grant and by the Hermann Minkowski Minerva Center for Geometry at Tel Aviv University.

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Alon, N. Additive latin transversals. Isr. J. Math. 117, 125–130 (2000). https://doi.org/10.1007/BF02773567

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  • DOI: https://doi.org/10.1007/BF02773567

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