Coherent configurations over copies of association schemes of prime order

2013/09/15 by Sharafdini, Reza, Hirasaka, Mitsugu
#05C10 #05C15 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1309.3725

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 |Ω₁|=|Ω₂| 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|=|Ω₁|=|Ω₂| for some (α,β)∈ Ω₁× Ω₂. 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.

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