Geodesic
Proof of an intersection theorem via graph homomorphisms
The electronic journal of combinatorics, Tome 13 (2006)

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Zbl EuDML
Let $0 \leq p \leq 1/2 $ and let $\{0,1\}^n$ be endowed with the product measure $\mu_p$ defined by $\mu_p(x)=p^{|x|}(1-p)^{n-|x|}$, where $|x|=\sum x_i$. Let $I \subseteq \{0,1\}^n$ be an intersecting family, i.e. for every $x, y \in I$ there exists a coordinate $1 \leq i \leq n$ such that $x_i=y_i=1$. Then $\mu_p(I) \leq p.$ Our proof uses measure preserving homomorphisms between graphs.
DOI : 10.37236/1144
Classification : 05D05 
Irit Dinur; Ehud Friedgut. Proof of an intersection theorem via graph homomorphisms. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1144
@article{10_37236_1144,
     author = {Irit Dinur and Ehud Friedgut},
     title = {Proof of an intersection theorem via graph homomorphisms},
     journal = {The electronic journal of combinatorics},
     year = {2006},
     volume = {13},
     doi = {10.37236/1144},
     zbl = {1087.05060},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1144/}
}
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