$s$-almost cross-$t$-intersecting families for finite sets
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908425464578048 |
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| author | Liu, Dehai Wang, Kaishun Yao, Tian |
| author_facet | Liu, Dehai Wang, Kaishun Yao, Tian |
| contents | Two families $\mathcal{F}$ and $\mathcal{G}$ of $k$-subsets of an $n$-set are called $s$-almost cross-$t$-intersecting if each member in $\mathcal{F}$ (resp. $\mathcal{G}$) is $t$-disjoint with at most $s$ members in $\mathcal{G}$ (resp. $\mathcal{F}$). In this paper, we characterize the $s$-almost cross-$t$-intersecting families with the maximum product of their sizes. Furthermore, we provide a corresponding stability result after studying the $s$-almost cross-$t$-intersecting families which are not cross-$t$-intersecting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_21993 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $s$-almost cross-$t$-intersecting families for finite sets Liu, Dehai Wang, Kaishun Yao, Tian Combinatorics 05D05 Two families $\mathcal{F}$ and $\mathcal{G}$ of $k$-subsets of an $n$-set are called $s$-almost cross-$t$-intersecting if each member in $\mathcal{F}$ (resp. $\mathcal{G}$) is $t$-disjoint with at most $s$ members in $\mathcal{G}$ (resp. $\mathcal{F}$). In this paper, we characterize the $s$-almost cross-$t$-intersecting families with the maximum product of their sizes. Furthermore, we provide a corresponding stability result after studying the $s$-almost cross-$t$-intersecting families which are not cross-$t$-intersecting. |
| title | $s$-almost cross-$t$-intersecting families for finite sets |
| topic | Combinatorics 05D05 |
| url | https://arxiv.org/abs/2506.21993 |