On the intersecting family process
Fuente:
arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866911791970254848 |
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| author | Bennett, Patrick Frieze, Alan Newman, Andrew Pegden, Wesley |
| author_facet | Bennett, Patrick Frieze, Alan Newman, Andrew Pegden, Wesley |
| contents | We study the intersecting family process initially studied in \cite{BCFMR}. Here $k=k(n)$ and $E_1,E_2,\ldots,E_m$ is a random sequence of $k$-sets from $\binom{[n]}{k}$ where $E_{r+1}$ is uniformly chosen from those $k$-sets that are not already chosen and that meet $E_i,i=1,2,\ldots,r$. We prove some new results for the case where $k=cn^{1/3}$ and for the case where $k\gg n^{1/2}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_09050 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the intersecting family process Bennett, Patrick Frieze, Alan Newman, Andrew Pegden, Wesley Combinatorics Probability We study the intersecting family process initially studied in \cite{BCFMR}. Here $k=k(n)$ and $E_1,E_2,\ldots,E_m$ is a random sequence of $k$-sets from $\binom{[n]}{k}$ where $E_{r+1}$ is uniformly chosen from those $k$-sets that are not already chosen and that meet $E_i,i=1,2,\ldots,r$. We prove some new results for the case where $k=cn^{1/3}$ and for the case where $k\gg n^{1/2}$. |
| title | On the intersecting family process |
| topic | Combinatorics Probability |
| url | https://arxiv.org/abs/2302.09050 |