On symmetric 2-(70,24,8) designs with an automorphism of order 6
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909129000353792 |
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| author | Rukavina, Sanja Tonchev, Vladimir D. |
| author_facet | Rukavina, Sanja Tonchev, Vladimir D. |
| contents | In this paper we analyze possible actions of an automorphism of order six on a $2$-$(70, 24, 8)$ design, and give a complete classification for the action of the cyclic automorphism group of order six $G= \langle ρ\rangle \cong Z_6 \cong Z_2 \times Z_3$ where $ρ^3$ fixes exactly $14$ points (blocks) and $ρ^2$ fixes $4$ points (blocks). Up to isomorphism, there are $3718$ such designs. This result significantly increases the number of known $2$-$(70,24,8)$ designs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_01237 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On symmetric 2-(70,24,8) designs with an automorphism of order 6 Rukavina, Sanja Tonchev, Vladimir D. Combinatorics 05B05, 94B05 In this paper we analyze possible actions of an automorphism of order six on a $2$-$(70, 24, 8)$ design, and give a complete classification for the action of the cyclic automorphism group of order six $G= \langle ρ\rangle \cong Z_6 \cong Z_2 \times Z_3$ where $ρ^3$ fixes exactly $14$ points (blocks) and $ρ^2$ fixes $4$ points (blocks). Up to isomorphism, there are $3718$ such designs. This result significantly increases the number of known $2$-$(70,24,8)$ designs. |
| title | On symmetric 2-(70,24,8) designs with an automorphism of order 6 |
| topic | Combinatorics 05B05, 94B05 |
| url | https://arxiv.org/abs/2211.01237 |