A new sieve for restricted multiset counting

Abstract

The Li–Wan sieve [11] is extended to multisets when the underlying set is symmetric. The main ingredient of the proof is the Möbius inversion formula on the poset of partitions of {1,2,…,k} ordered by refinement. As illustrative applications, we investigate the problems of partitions over finite fields and zero-sum multisets over the additive group Z/nZ.