Automorphisms of the generalized cluster complex
We exhibit a dihedral symmetry in the generalized cluster complex defined by Fomin and Reading. Together with diagram symmetries, they generate the automorphism group of the complex. A consequence is a simple explicit formula for the order of this automorphism group.
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| Format: | Article |
| Language: | English |
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American Journal of Combinatorics
2025-04-01
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| Series: | The American Journal of Combinatorics |
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| Online Access: | https://ajcombinatorics.org/ojs/index.php/AmJC/article/view/29 |
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| _version_ | 1849699694386610176 |
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| author | Matthieu Josuat-Vergès |
| author_facet | Matthieu Josuat-Vergès |
| author_sort | Matthieu Josuat-Vergès |
| collection | DOAJ |
| description |
We exhibit a dihedral symmetry in the generalized cluster complex defined by Fomin and Reading. Together with diagram symmetries, they generate the automorphism group of the complex. A consequence is a simple explicit formula for the order of this automorphism group.
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| format | Article |
| id | doaj-art-1998801256fd407b8e85a2df8db5ad7a |
| institution | DOAJ |
| issn | 2768-4202 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | American Journal of Combinatorics |
| record_format | Article |
| series | The American Journal of Combinatorics |
| spelling | doaj-art-1998801256fd407b8e85a2df8db5ad7a2025-08-20T03:18:31ZengAmerican Journal of CombinatoricsThe American Journal of Combinatorics2768-42022025-04-01410.63151/amjc.v4i.29Automorphisms of the generalized cluster complexMatthieu Josuat-Vergès We exhibit a dihedral symmetry in the generalized cluster complex defined by Fomin and Reading. Together with diagram symmetries, they generate the automorphism group of the complex. A consequence is a simple explicit formula for the order of this automorphism group. https://ajcombinatorics.org/ojs/index.php/AmJC/article/view/29Cluster complexFinite Coxeter groupAutomorphism groupDihedral groupSymmetry |
| spellingShingle | Matthieu Josuat-Vergès Automorphisms of the generalized cluster complex The American Journal of Combinatorics Cluster complex Finite Coxeter group Automorphism group Dihedral group Symmetry |
| title | Automorphisms of the generalized cluster complex |
| title_full | Automorphisms of the generalized cluster complex |
| title_fullStr | Automorphisms of the generalized cluster complex |
| title_full_unstemmed | Automorphisms of the generalized cluster complex |
| title_short | Automorphisms of the generalized cluster complex |
| title_sort | automorphisms of the generalized cluster complex |
| topic | Cluster complex Finite Coxeter group Automorphism group Dihedral group Symmetry |
| url | https://ajcombinatorics.org/ojs/index.php/AmJC/article/view/29 |
| work_keys_str_mv | AT matthieujosuatverges automorphismsofthegeneralizedclustercomplex |