Cross-intersection theorems for uniform partitions of finite sets
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912609295400960 |
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| author | Yao, Tian Cao, Mengyu Zhang, Haixiang |
| author_facet | Yao, Tian Cao, Mengyu Zhang, Haixiang |
| contents | A set partition is $c$-uniform if every block has size $c$. Two families of $c$-uniform partitions of a finite set are said to be cross $t$-intersecting if two partitions from different families share at least $t$ blocks. In this paper, we establish some product-type extremal results for such cross $t$-intersecting families. Our results yield an Erdős-Ko-Rado theorem and a Hilton-Milner theorem for uniform set partitions. Additionally, cross $t$-intersecting families with the maximum sum of their sizes are also characterized. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_17188 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cross-intersection theorems for uniform partitions of finite sets Yao, Tian Cao, Mengyu Zhang, Haixiang Combinatorics 05D05 A set partition is $c$-uniform if every block has size $c$. Two families of $c$-uniform partitions of a finite set are said to be cross $t$-intersecting if two partitions from different families share at least $t$ blocks. In this paper, we establish some product-type extremal results for such cross $t$-intersecting families. Our results yield an Erdős-Ko-Rado theorem and a Hilton-Milner theorem for uniform set partitions. Additionally, cross $t$-intersecting families with the maximum sum of their sizes are also characterized. |
| title | Cross-intersection theorems for uniform partitions of finite sets |
| topic | Combinatorics 05D05 |
| url | https://arxiv.org/abs/2509.17188 |