On the maximum number of distinct intersections in an intersecting family
| Autor: | Peter Frankl, Sergei Kiselev, Andrey Kupavskii |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: | |
| Popis: | For $n > 2k \geq 4$ we consider intersecting families $\mathcal F$ consisting of $k$-subsets of $\{1, 2, \ldots, n\}$. Let $\mathcal I(\mathcal F)$ denote the family of all distinct intersections $F \cap F'$, $F \neq F'$ and $F, F'\in \mathcal F$. Let $\mathcal A$ consist of the $k$-sets $A$ satisfying $|A \cap \{1, 2, 3\}| \geq 2$. We prove that for $n \geq 50 k^2$ $|\mathcal I(\mathcal F)|$ is maximized by $\mathcal A$. |
| Databáze: | OpenAIRE |
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