Transversals of additive Latin squares

Published

Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Dasgupta, S; Károlyi, G; Serra, O; Szegedy, B

Published Date

  • January 1, 2001

Published In

Volume / Issue

  • 126 /

Start / End Page

  • 17 - 28

Electronic International Standard Serial Number (EISSN)

  • 1565-8511

International Standard Serial Number (ISSN)

  • 0021-2172

Digital Object Identifier (DOI)

  • 10.1007/BF02784149

Citation Source

  • Scopus