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Publications [#338522] of Samit Dasgupta

Papers Published

  1. Dasgupta, S; Károlyi, G; Serra, O; Szegedy, B, Transversals of additive Latin squares, Israel Journal of Mathematics, vol. 126 no. 1 (January, 2001), pp. 17-28, Springer Nature [doi]
    (last updated on 2019/05/19)

    Abstract:
    Let A = {a 1 ,..., a k } and B = {b 1 ,..., b k } be two subsets of an Abelian group G, k ≤ |G|. Snevily conjectured that, when G is of odd order, there is a permutation π ≤ S k such that the sums a i + b π(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 (Z p ) α and Z pα in the case k < p, and verify Snevily's conjecture for every cyclic group of odd order.

 

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