The synchronisation hierarchy via coherent configurations

Bamberg, John, & Lansdown, Jesse. (2026). The synchronisation hierarchy via coherent configurations. Linear Algebra and its Applications, 735, 203-221. https://doi.org/10.1016/j.laa.2026.01.013

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 I-group. We also consider design-orthogonality more generally for noncommutative homogeneous coherent configurations.

Funder

Australian Research Council
Faculty of Engineering, University of Canterbury
University of Western Australia

Publisher

Elsevier

Rights

CC BY

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