The synchronisation hierarchy via coherent configurations
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913424531783680 |
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| author | Bamberg, John Lansdown, Jesse |
| author_facet | Bamberg, John Lansdown, Jesse |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07352 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The synchronisation hierarchy via coherent configurations Bamberg, John Lansdown, Jesse Combinatorics 20B15, 05E16, 05E30 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. |
| title | The synchronisation hierarchy via coherent configurations |
| topic | Combinatorics 20B15, 05E16, 05E30 |
| url | https://arxiv.org/abs/2407.07352 |