Regular sets of lines in rank 3 polar spaces
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910486626304000 |
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| author | Ihringer, Ferdinand Rodgers, Morgan |
| author_facet | Ihringer, Ferdinand Rodgers, Morgan |
| contents | There are 6 families of finite polar spaces of rank $3$.
The set of lines in a rank $3$ polar space form a rank $5$ association scheme.
We determine the regular sets of minimal size in several of these polar spaces, and describe some examples.
We also give a new family of Cameron--Liebler sets of generators in the polar spaces $O^+(10,q)$ when $q = 3^h$ using a regular set of lines in $O(7,q)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_02397 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Regular sets of lines in rank 3 polar spaces Ihringer, Ferdinand Rodgers, Morgan Combinatorics 05B25, 05E30, 51A50, 51E20 There are 6 families of finite polar spaces of rank $3$. The set of lines in a rank $3$ polar space form a rank $5$ association scheme. We determine the regular sets of minimal size in several of these polar spaces, and describe some examples. We also give a new family of Cameron--Liebler sets of generators in the polar spaces $O^+(10,q)$ when $q = 3^h$ using a regular set of lines in $O(7,q)$. |
| title | Regular sets of lines in rank 3 polar spaces |
| topic | Combinatorics 05B25, 05E30, 51A50, 51E20 |
| url | https://arxiv.org/abs/2312.02397 |