A Snevily-type inequality for multisets

Abstract

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