http://www.cnr.it/ontology/cnr/individuo/prodotto/ID7047
Delta-systems and qualitative (in)dependence (Articolo in rivista)
- Type
- Label
- Delta-systems and qualitative (in)dependence (Articolo in rivista) (literal)
- Anno
- 2002-01-01T00:00:00+01:00 (literal)
- Alternative label
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- Korner, J.; Monti, A. (literal)
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- Pagina fine
- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
- Rivista
- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#note
- Note
- ISI Web of Science (WOS) (literal)
- Titolo
- Delta-systems and qualitative (in)dependence (literal)
- Abstract
- Following Erdos and Rado, three sets are said to form a \"deltatriple\" if any two of them have the same intersection. Let $F(n, 3)$ denote the largest cardinality of a family of subsets of an $n$--set not containing a delta--triple. It is not known whether $\limsup_{n \rightarrow \infty} n^{-1} \log F(n, 3)<1$. We say that a family of bipartitionsof an $n$--set is qualitatively 3/4-weakly 3--dependent if the common refinement of any 3 distinct partitions of the family has at least 6 non--empty classes, (i. e., at least 3/4 of the total.) Let $I(n)$ denote the maximum cardinality of such a family. We derive a simple relation between the exponential asymptotics of $F(n, 3)$ and $I(n)$ and show, as a consequence, that $\limsup_{n\rightarrow \infty} n^{-1} \log F(n,3)=1$ if and only if $\limsup_{n \rightarrow \infty}n^{-1} \log I(n)=1.$ (literal)
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- Autore CNR
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