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Proof of an Intersection Theorem via Graph Homomorphisms
Journal article   an open version is available  Peer reviewed

Proof of an Intersection Theorem via Graph Homomorphisms

Irit Dinur and Ehud Friedgut
The Electronic journal of combinatorics, Vol.13(1), pp.1-4
21/Mar/2006
url
https://doi.org/10.37236/1144View
Published (Version of record)Free to read and download Open Access

Abstract

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.

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