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A subset $A$ of $[n] = \{1, \dots, n\}$ is $k$-separated if, when theelements of $[n]$ are considered on a circle, between any two elements of $A$there are at least $k$ elements of $[n]$ that are not in $A$. A family$\mathcal{A}$ of sets is intersecting if every two sets in $\mathcal{A}$intersect. We give a short and simple proof of a remarkable result of Talbot(2003), stating that if $n \geq (k + 1)r$ and $\mathcal{A}$ is an intersectingfamily of $k$-separated $r$-element subsets of $[n]$, then $|\mathcal{A}| \leq\binom{n - kr - 1}{r - 1}$. This bound is best possible.

A simple proof of Talbot's theorem for intersecting separated sets