Fusions of tensor powers of Johnson schemes

Eberhard, Sean; Muzychuk, Mikhail

doi:10.5802/alco.271

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Fusions of tensor powers of Johnson schemes

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)

Algebraic Combinatorics, Tome 6 (2023) no. 2, pp. 533-538

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Résumé

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 $ℋ (d, m)$ . 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 $ℋ (d / e, m^{e})$ for some $e ∣ d$ . This note answers this question positively provided that $m$ is large enough. We similarly classify primitive fusions of the $d$ th tensor power of a Johnson scheme on $(\binom{m}{k})$ points when $m$ is large enough in terms of $k$ and $d$ .

Reçu le : 2022-05-30
Révisé le : 2022-09-21
Accepté le : 2022-09-27
Publié le : 2023-05-03

DOI : 10.5802/alco.271

Classification : 05E30
Keywords: association schemes, permutation groups

Affiliations des auteurs :

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)

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Fusions of tensor powers of {Johnson} schemes},
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Eberhard, Sean; Muzychuk, Mikhail. Fusions of tensor powers of Johnson schemes. Algebraic Combinatorics, Tome 6 (2023) no. 2, pp. 533-538. doi: 10.5802/alco.271

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