A character theoretic formula for base size II
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912319645155328 |
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| author | del Valle, Coen |
| author_facet | del Valle, Coen |
| contents | A base for a permutation group $G$ acting on a set $Ω$ is a sequence $\mathcal{B}$ of points of $Ω$ such that the pointwise stabiliser $G_{\mathcal{B}}$ is trivial. The base size of $G$ is the size of a smallest base for $G$. Extending the results of a recent paper of the author, we prove a 2013 conjecture of Fritzsche, Külshammer, and Reiche. Moreover, we generalise this conjecture and derive an alternative character theoretic formula for the base size of a certain class of permutation groups. As a consequence of our work, a third formula for the base size of the symmetric group of degree $n$ acting on the subsets of $\{1,2,\dots, n\}$ is obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07832 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A character theoretic formula for base size II del Valle, Coen Group Theory Representation Theory A base for a permutation group $G$ acting on a set $Ω$ is a sequence $\mathcal{B}$ of points of $Ω$ such that the pointwise stabiliser $G_{\mathcal{B}}$ is trivial. The base size of $G$ is the size of a smallest base for $G$. Extending the results of a recent paper of the author, we prove a 2013 conjecture of Fritzsche, Külshammer, and Reiche. Moreover, we generalise this conjecture and derive an alternative character theoretic formula for the base size of a certain class of permutation groups. As a consequence of our work, a third formula for the base size of the symmetric group of degree $n$ acting on the subsets of $\{1,2,\dots, n\}$ is obtained. |
| title | A character theoretic formula for base size II |
| topic | Group Theory Representation Theory |
| url | https://arxiv.org/abs/2504.07832 |