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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/2405.02577 |
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| _version_ | 1866929335467769856 |
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| author | Zhou, Jiang |
| author_facet | Zhou, Jiang |
| contents | In the classical probability model, let $f(n)$ be the maximum number of pairwise independent events for the sample space with $n$ sample points. The determination of $f(n)$ is equivalent to the problem of determining the maximum cardinality of specific intersecting families on the set $\{1,2,\ldots,n\}$ . We show that $f(n)\leq n+1$, and $f(n)=n+1$ if there exists a Hadamard matrix of order $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02577 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A combinatorial problem related to the classical probability Zhou, Jiang Combinatorics Probability In the classical probability model, let $f(n)$ be the maximum number of pairwise independent events for the sample space with $n$ sample points. The determination of $f(n)$ is equivalent to the problem of determining the maximum cardinality of specific intersecting families on the set $\{1,2,\ldots,n\}$ . We show that $f(n)\leq n+1$, and $f(n)=n+1$ if there exists a Hadamard matrix of order $n$. |
| title | A combinatorial problem related to the classical probability |
| topic | Combinatorics Probability |
| url | https://arxiv.org/abs/2405.02577 |