Fusions of tensor powers of Johnson schemes
Algebraic Combinatorics, Volume 6 (2023) no. 2, pp. 533-538.

This paper is a follow-up to [5], in which the first author studied primitive association schemes lying between a tensor power 𝒯 m d of the trivial association scheme and the Hamming scheme (d,m). A question which arose naturally in that study was whether all primitive fusions of 𝒯 m d lie between 𝒯 m e d/e and (d/e,m e ) for some ed. This note answers this question positively provided that m is large enough. We similarly classify primitive fusions of the dth tensor power of a Johnson scheme on m k points when m is large enough in terms of k and d.

Published online:
DOI: 10.5802/alco.271
Classification: 05E30
Keywords: association schemes, permutation groups
Eberhard, Sean 1; Muzychuk, Mikhail 2

1 Centre for Mathematical Sciences Wilberforce Road Cambridge CB3 0WB (U.K.)
2 Department of Mathematics Ben Gurion University P.O.B. 653, Beer Sheva 8410501 (Israel)
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Eberhard, Sean; Muzychuk, Mikhail. Fusions of tensor powers of Johnson schemes. Algebraic Combinatorics, Volume 6 (2023) no. 2, pp. 533-538. doi : 10.5802/alco.271. https://alco.centre-mersenne.org/articles/10.5802/alco.271/

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