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
   (last updated on 2024/04/19)

   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.