Enumeration Techniques on Cyclic Schur Rings

This paper is based on the results of the 2020 Ural Workshop on Group Theory and Combinatorics. Any Schur ring is uniquely determined by a partition of the elements of the group. In this paper we present a general technique for enumerating Schur rings over cyclic groups using traditional Schur rings. We also survey recent efforts to enumerate Schur rings over cyclic groups of specific orders.