Coherent configurations over copies of association schemes of prime order

Reza Sharafdini, Mitsugu Hirasaka

Abstract


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.


Keywords


Coherent configurations, association schemes, prime order, symmetric designs

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ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications