AMS: 20c05, 05c25, 05e30, 05a15 05e16 20k27
DOI: 10.21538/0134-4889-2021-27-4-276-289
Full text
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
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Received November 24, 2020
Revised September 13, 2021
Accepted September 17, 2021
Andrew Misseldine, Prof., Mathematics department at Southern Utah University, USA (Utah), e-mail: andrewmisseldine@suu.edu
Cite this article as: Andrew Misseldine, Enumeration Techniques on Cyclic Schur Rings, Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2021, vol. 27, no. 4, pp. 276–289.
Русский
Э. Мисселдин. О подсчете числа колец Шура над циклическими группами
Любое кольцо Шура однозначно определяется разбиением группы. В статье предложен общий метод подсчета числа колец Шура над циклическими группами, использующий традиционные кольца Шура. Приведен обзор недавних исследований, посвященных подсчету числа колец Шура над циклическими группами некоторых порядков.
Ключевые слова: кольцо Шура, циклическая группа, ассоциативная схема, решетка подгрупп
