Zero sum sets in abelian groups
Minjia Shi, Denis S. Krotov, Xiaoxiao Li, Patrick Solé · arXiv (Cornell University) · 2021
The distribution of cardinalities of zero-sum sets in abelian groups is completely determined. A complex summation involving the Möbius function is given for the general abelian group, while in many special cases, including the case of elementary abelian groups, solved earlier by Li and Wan, it has a compact form. The proof involves two different Möbius transforms, on positive integers and on set partitions.