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The synchronisation hierarchy via coherent configurations

2024/07/10 by John Bamberg, Bamberg, John, Jesse Lansdown +1
Computer Science · #05E16 #05E30 #20B15 #Combinatorics (math.CO) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation

paper · doi:10.48550/arxiv.2407.07352

openalex publication_date 2024/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We describe the spreading property for finite transitive permutation groups in terms of properties of their associated coherent configurations, in much the same way that separating and synchronising groups can be described via properties of their orbital graphs. We also show how the other properties in the synchronisation hierarchy naturally fit inside this framework. This combinatorial description allows for more efficient computational tools, and we deduce that every spreading permutation group of degree at most 8191 is a ℚI-group. We also consider design-orthogonality more generally for noncommutative homogeneous coherent configurations.

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