Cardinalities of irredundant bases of finite primitive groups
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913452606357504 |
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| author | Mastrogiacomo, Fabio |
| author_facet | Mastrogiacomo, Fabio |
| contents | Let $G$ be a finite permutation group acting on a set $Ω$. An ordered sequence $(ω_1,\ldots,ω_\ell)$ of elements of $Ω$ is an irredundant base for $G$ if the pointwise stabilizer of the sequence is trivial and no point is fixed by the stabilizer of its predecessors. We show that any interval of natural numbers can be realized as the set of cardinalities of irredundant bases for some finite primitive group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20849 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cardinalities of irredundant bases of finite primitive groups Mastrogiacomo, Fabio Group Theory Combinatorics Let $G$ be a finite permutation group acting on a set $Ω$. An ordered sequence $(ω_1,\ldots,ω_\ell)$ of elements of $Ω$ is an irredundant base for $G$ if the pointwise stabilizer of the sequence is trivial and no point is fixed by the stabilizer of its predecessors. We show that any interval of natural numbers can be realized as the set of cardinalities of irredundant bases for some finite primitive group. |
| title | Cardinalities of irredundant bases of finite primitive groups |
| topic | Group Theory Combinatorics |
| url | https://arxiv.org/abs/2407.20849 |