Math @ Duke

Publications [#338522] of Samit Dasgupta
Papers Published
 Dasgupta, S; Károlyi, G; Serra, O; Szegedy, B, Transversals of additive Latin squares,
Israel Journal of Mathematics, vol. 126 no. 1
(January, 2001),
pp. 1728, Springer Nature [doi]
(last updated on 2020/08/13)
Abstract: Let A = {a1,..., ak} and B = {b1,..., bk} be two subsets of an Abelian group G, k ≤ G. Snevily conjectured that, when G is of odd order, there is a permutation π ≤ Sk such that the sums ai + bπ(i), 1 ≤ i ≤ k, are pairwise different. Alon showed that the conjecture is true for groups of prime order, even when A is a sequence of k < G elements, i.e., by allowing repeated elements in A. In this last sense the result does not hold for other Abelian groups. With a new kind of application of the polynomial method in various finite and infinite fields we extend Alon's result to the groups (Zp)α and Zpα in the case k < p, and verify Snevily's conjecture for every cyclic group of odd order.


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