Additive latin transversals |
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Authors: | Noga Alon |
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Institution: | (1) Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978 Tel Aviv, Israel;(2) Institute for Advanced Study, 08540 Princeton, NJ, USA |
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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.
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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Keywords: | |
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