| Autor: |
Maleki, Roghayeh, Razafimahatratra, Andriaherimanana Sarobidy |
| Rok vydání: |
2024 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
Let $p$ be a prime and $q = p^k$. A subset $\mathcal{F} \subset \operatorname{\Gamma L}_{2}(q)$ is intersecting if any two semilinear transformations in $\mathcal{F}$ agree on some non-zero vector in $\mathbb{F}_q^2$. We show that any intersecting set of $\operatorname{\Gamma L}_{2}(q)$ is of size at most that of a stabilizer of a non-zero vector, and we characterize the intersecting sets of this size. Our proof relies on finding a subgraph which is a lexicographic product in the derangement graph of $\operatorname{\Gamma L}_{2}(q)$ in its action on non-zero vectors of $\mathbb{F}_q^2$. This method is also applied to give a new proof that the only maximal intersecting sets of $\operatorname{GL}_{2}(q)$ are the maximum intersecting sets. |
| Databáze: |
arXiv |
| Externí odkaz: |
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