= Cyclic interval intersection bound
An <intersecting family> of cyclic intervals of length $r$ in a cyclic order of $n$ positions has at most $r$ members when $1\leq r\leq n/2$. Rotate one selected interval to end at position $n$. Intervals ending at $r,\ldots,n-r$ miss it. Pair the remaining endpoints, other than $n$, as $(j,j+n-r)$ for $1\leq j\leq r-1$; each pair represents two disjoint intervals, hence contributes at most one member. This gives $1+(r-1)=r$. Counting such intervals over all <permutations> proves the <Erdős-Ko-Rado theorem>.
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