Enumeration Techniques on Cyclic Schur Rings

TL;DR

This paper introduces a general enumeration technique for Schur rings over cyclic groups and reviews recent progress in enumerating such rings for specific group orders.

Contribution

It presents a new general method for enumerating Schur rings over cyclic groups and surveys recent enumeration results for particular group orders.

Findings

Developed a general enumeration technique for cyclic Schur rings.

Surveyed recent enumeration efforts for specific cyclic group orders.

Provides insights into the structure and classification of cyclic Schur rings.

Abstract

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.