A new sieve for restricted multiset counting

Abstract: The Li--Wan sieve is extended to multisets when the underlying set is symmetric. The main ingredient of the proof is the Mobius inversion formula on the poset of partitions of ${1,2,\dots,k}$ ordered by refinement. As illustrative applications, we investigate the problems of partitions over finite fields and zero-sum multisets over the additive group $\mathbb{Z}/n\mathbb{Z}$. .