Fusions of tensor powers of Johnson schemes

Sean Eberhard, Mikhail Muzychuk

Research output: Contribution to journalArticlepeer-review


This paper is a follow-up to [5], in which the first author studied primitive association schemes lying between a tensor power Tmd 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 Tmd lie between Tmd/e e and H(d/e, me) for some e | d. 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 (mk ) points when m is large enough in terms of k and d.

Original languageEnglish
Pages (from-to)533-538
Number of pages6
JournalAlgebraic Combinatorics
Issue number2
StatePublished - 1 Jan 2023


  • association schemes
  • permutation groups

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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