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arXiv · 2407.07352

The synchronisation hierarchy via coherent configurations

John Bamberg·Jesse Lansdown
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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 $\mathbb{Q}$I-group. We also consider design-orthogonality more generally for noncommutative homogeneous coherent configurations.

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John Bamberg, Jesse Lansdown. 2024-07-10. The synchronisation hierarchy via coherent configurations. https://arxiv.org/abs/2407.07352

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