PROBABILISTIC METHODS IN COMBINATORICS 1. Introduction ...
PROBABILISTIC METHODS IN COMBINATORICS 1. Introduction ...
PROBABILISTIC METHODS IN COMBINATORICS 1. Introduction ...
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
4 YUFEI ZHAO<br />
Since F is intersecting, there are at most k continguous sets in F. Indeed, suppose that A ∈ F<br />
is contiguous. Then there are 2(k − 1) other contingous sets (not necessarily in F) that intersect A,<br />
but they can be paired off into disjoint pairs. Since F is intersecting, it follows that it contains at<br />
most k continguous sets. Combining with result from the previous paragraph, we see that n|F|<br />
( n k) ≤ k,<br />
and hence |F| ≤ n( k n<br />
) (<br />
k = n−1<br />
k−1)<br />
. □
Change language