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The synchronisation hierarchy via coherent configurations.

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Title: The synchronisation hierarchy via coherent configurations.
Authors: Bamberg, John1 (AUTHOR) john.bamberg@uwa.edu.au, Lansdown, Jesse1,2 (AUTHOR) jesse.lansdown@universityofgalway.ie
Source: Linear Algebra & its Applications. Apr2026, Vol. 735, p203-221. 19p.
Subjects: Synchronization, Permutation groups, Combinatorial designs & configurations, Graph theory
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 Q I-group. We also consider design-orthogonality more generally for noncommutative homogeneous coherent configurations. [ABSTRACT FROM AUTHOR]
Copyright of Linear Algebra & its Applications is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 191426586
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: The synchronisation hierarchy via coherent configurations.
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  Data: <searchLink fieldCode="AR" term="%22Bamberg%2C+John%22">Bamberg, John</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> john.bamberg@uwa.edu.au</i><br /><searchLink fieldCode="AR" term="%22Lansdown%2C+Jesse%22">Lansdown, Jesse</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> jesse.lansdown@universityofgalway.ie</i>
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  Data: <searchLink fieldCode="JN" term="%22Linear+Algebra+%26+its+Applications%22">Linear Algebra & its Applications</searchLink>. Apr2026, Vol. 735, p203-221. 19p.
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  Data: <searchLink fieldCode="DE" term="%22Synchronization%22">Synchronization</searchLink><br /><searchLink fieldCode="DE" term="%22Permutation+groups%22">Permutation groups</searchLink><br /><searchLink fieldCode="DE" term="%22Combinatorial+designs+%26+configurations%22">Combinatorial designs & configurations</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink>
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  Data: 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 Q I-group. We also consider design-orthogonality more generally for noncommutative homogeneous coherent configurations. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Linear Algebra & its Applications is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1016/j.laa.2026.01.013
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      – Code: eng
        Text: English
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        PageCount: 19
        StartPage: 203
    Subjects:
      – SubjectFull: Synchronization
        Type: general
      – SubjectFull: Permutation groups
        Type: general
      – SubjectFull: Combinatorial designs & configurations
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      – SubjectFull: Graph theory
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      – TitleFull: The synchronisation hierarchy via coherent configurations.
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            NameFull: Bamberg, John
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            NameFull: Lansdown, Jesse
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            – D: 15
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              Text: Apr2026
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              Y: 2026
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