Geodesic
Coherent configurations over copies of association schemes of prime order
Ars Mathematica Contemporanea, Tome 12 (2017) no. 1, pp. 111-126.

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Let G be a group acting faithfully and transitively on Ω i for i = 1, 2. A famous theorem by Burnside implies the following fact: If ∣Ω 1∣ = ∣Ω 2∣ is a prime and the rank of one of the actions is greater than two, then the actions are equivalent, or equivalently ∣(α, β)G∣ = ∣Ω 1∣ = ∣Ω 2∣ for some (α, β) ∈ Ω 1 × Ω 2.In this paper we consider a combinatorial analogue to this fact through the theory of coherent configurations, and give some arithmetic sufficient conditions for a coherent configuration with two homogeneous components of prime order to be uniquely determined by one of the homogeneous components.
DOI : 10.26493/1855-3974.769.47d
Keywords: Coherent configurations, association schemes, prime order, symmetric designs 
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Reza Sharafdini; Mitsugu Hirasaka. Coherent configurations over copies of association schemes of prime order. Ars Mathematica Contemporanea, Tome 12 (2017) no. 1, pp. 111-126. doi : 10.26493/1855-3974.769.47d. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.769.47d/

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