A Snevily-type inequality for multisets (Q2043675)

\textit{N. Alon} [Isr. J. Math. 117, 125--130 (2000; Zbl 1047.11019)] proved that if \(p\) is an odd prime, \(1 \leq n<p\) and \(a_1, \ldots ,a_n\) are distinct elements in \(\mathbb Z_p\) and \(b_1, \ldots, b_n\) are arbitrary elements in \(\mathbb Z_p\), then there exists a permutation \(\sigma\) 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, the authors present a multiset variant of this result. The authors remark that these theorems are not true for \(n = p\).