Symmetric 2-(35,17,8) designs with an automorphism of order 2
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912279887347712 |
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| author | Rukavina, Sanja Tonchev, Vladimir D. |
| author_facet | Rukavina, Sanja Tonchev, Vladimir D. |
| contents | The largest prime p that can be the order of an automorphism of a 2-(35,17,8) design is p=17, and all 2-(35,17,8) designs with an automorphism of order 17 were classified by Tonchev. The symmetric 2-(35,17,8) designs with automorphisms of odd prime order $p<17$ were also classified. In this paper we give the classification of all symmetric 2-(35,17,8) designs that admit an automorphism of order $p=2$. It is shown that there are exactly $11,642,495$ nonisomorphic such designs. Furthermore, it is shown that the number of nonisomorphic 3-(36,18,8) designs which have at least one derived 2-$(35,17,8)$ design with an automorphism of order 2, is $1,015,225$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_13722 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symmetric 2-(35,17,8) designs with an automorphism of order 2 Rukavina, Sanja Tonchev, Vladimir D. Combinatorics 05B05 The largest prime p that can be the order of an automorphism of a 2-(35,17,8) design is p=17, and all 2-(35,17,8) designs with an automorphism of order 17 were classified by Tonchev. The symmetric 2-(35,17,8) designs with automorphisms of odd prime order $p<17$ were also classified. In this paper we give the classification of all symmetric 2-(35,17,8) designs that admit an automorphism of order $p=2$. It is shown that there are exactly $11,642,495$ nonisomorphic such designs. Furthermore, it is shown that the number of nonisomorphic 3-(36,18,8) designs which have at least one derived 2-$(35,17,8)$ design with an automorphism of order 2, is $1,015,225$. |
| title | Symmetric 2-(35,17,8) designs with an automorphism of order 2 |
| topic | Combinatorics 05B05 |
| url | https://arxiv.org/abs/2503.13722 |