Selecting k objects from a cycle with p pairs of separation s (Q797581)

Generalizing a result of \textit{J. Konvalina} [ibid. 31, 101-107 (1981; Zbl 0469.05003)], the author determines the number of ways a k-element subset can be chosen from a cyclically ordered n-set without two points of distance \(s\geq 1\). For \(n\geq 1+km\) where \(m=(s,n)\), the formula reduces to \((n/k)\binom{n-k-1}{k-1}.\)