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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.14714 |
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| _version_ | 1866914924937084928 |
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| author | Tricot, Paul |
| author_facet | Tricot, Paul |
| contents | The group $PGL(2,q)$ acts $3$-transitively on the projective line $GF(q) \cup \{\infty\}$. Thus, an orbit of its action on the $k$-subsets of the projective line is the block set of a $3$-$(q+1,k,λ)$ design. We find the parameters of the designs formed by the orbit of a block of the form $\langle θ^r \rangle$ or $\langle θ^r \rangle \cup \{ 0\}$, where $θ$ is a primitive element of $GF(q)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14714 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On $3$-designs from $PGL(2,q)$ Tricot, Paul Combinatorics The group $PGL(2,q)$ acts $3$-transitively on the projective line $GF(q) \cup \{\infty\}$. Thus, an orbit of its action on the $k$-subsets of the projective line is the block set of a $3$-$(q+1,k,λ)$ design. We find the parameters of the designs formed by the orbit of a block of the form $\langle θ^r \rangle$ or $\langle θ^r \rangle \cup \{ 0\}$, where $θ$ is a primitive element of $GF(q)$. |
| title | On $3$-designs from $PGL(2,q)$ |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2408.14714 |