Cyclic interval
= Cyclic interval
{title2=$I_j^{(r)}$}
A <cyclic interval> of length $r$ is the set of $r$ consecutive positions in a <cyclic ordering>. For $1\leq r<n$, there are $n$ distinct intervals, one ending at each position. Under a uniformly random <permutation>, a fixed $r$-set appears as an interval with probability $n/\binom nr$. This is the counting mechanism of the <Katona circle method>.