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Commutative Schur rings over symmetric groups

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Abstract

We study commutative Schur rings over the symmetric group \(S_n\) that contain the sum of the transpositions in \(S_n\), by determining the possibilities for the partition of the class of transpositions that such a Schur ring gives. We note a connection with Gallai colorings of complete graphs.

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Acknowledgments

The author wishes to thank the referees for their useful comments. All calculations made in the preparation of this paper were accomplished using MAGMA [9].

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  1. Department of Mathematics, Brigham Young University, Provo, UT, 84602, USA

    Stephen P. Humphries

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  1. Stephen P. Humphries
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Correspondence to Stephen P. Humphries.

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Humphries, S.P. Commutative Schur rings over symmetric groups. J Algebr Comb 42, 971–997 (2015). https://doi.org/10.1007/s10801-015-0613-2

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  • DOI: https://doi.org/10.1007/s10801-015-0613-2

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