A uniform version of a theorem by Lindström
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915819911380992 |
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| author | Hegedüs, Gábor |
| author_facet | Hegedüs, Gábor |
| contents | We prove the following uniform version of a theorem by Lindström:
Let $\mbox{$\cal F$}:=\{F_i:~ i\in I\}$ be a $k$-uniform set family of $[n]$, where $k\geq 1$. If $|\mbox{$\cal F$}|\geq n+1$, then there exist two disjoint subsets $I_1$ and $I_2$ of $I$ for which $$ \bigcup\limits_{i\in I_1} M_i=\bigcup\limits_{i\in I_2} M_i $$ and $$ \bigcap\limits_{i\in I_1} M_i=\bigcap\limits_{i\in I_2} M_i. $$ Our proof uses basic linear algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23009 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A uniform version of a theorem by Lindström Hegedüs, Gábor Combinatorics 05D05, 15A06, 15A03 We prove the following uniform version of a theorem by Lindström: Let $\mbox{$\cal F$}:=\{F_i:~ i\in I\}$ be a $k$-uniform set family of $[n]$, where $k\geq 1$. If $|\mbox{$\cal F$}|\geq n+1$, then there exist two disjoint subsets $I_1$ and $I_2$ of $I$ for which $$ \bigcup\limits_{i\in I_1} M_i=\bigcup\limits_{i\in I_2} M_i $$ and $$ \bigcap\limits_{i\in I_1} M_i=\bigcap\limits_{i\in I_2} M_i. $$ Our proof uses basic linear algebra. |
| title | A uniform version of a theorem by Lindström |
| topic | Combinatorics 05D05, 15A06, 15A03 |
| url | https://arxiv.org/abs/2602.23009 |