A Snevily-type inequality for multisets

Abstract

Alon [1] proved that if $$p$$\n is an odd prime, $$1\\le n < p$$\n and $$a_1,\\ldots,a_n$$\n are distinct elements in $$Z_p$$\n and $$b_1,\\ldots,b_n$$\n are arbitrary elements in $$Z_p$$\n then there exists a permutation of $$\\sigma$$\n of the indices $$1,\\ldots,n$$\n such that the elements $$a_1+b_{\\sigma(1)},\\ldots,a_n+b_{\\sigma(n)}$$\n are distinct. In this paper we present a multiset variant of this result.