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JOURNALS // Trudy Instituta Matematiki i Mekhaniki UrO RAN // Archive

Trudy Inst. Mat. i Mekh. UrO RAN, 2021 Volume 27, Number 4, Pages 276–289 (Mi timm1878)

Enumeration Techniques on Cyclic Schur Rings

A. Misseldine

Southern Utah University, Mathematics department

Abstract: 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.

Keywords: Schur ring; cyclic group; association scheme; lattice of subgroups.

Received: 24.11.2020
Revised: 13.09.2021
Accepted: 17.09.2021

Language: English

DOI: 10.21538/0134-4889-2021-27-4-276-289



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© Steklov Math. Inst. of RAS, 2024