Multicover Ucycles
A universal cycle, or Ucycle, for \(k\)-subsets of \([n]= \{1,2,\dots, n\}\) is a cyclic sequence of \((\begin{smallmatrix} n\\ k\end{smallmatrix})\) integers with the property that every \(k\)-subsets of \([n]\) appears exactly once consecutively in the sequence. A \(t\)-cover Ucycle for \(k\)-subsets of \([n]\) is a cyclic sequence of \(t(\begin{smallmatrix} n\\ k\end{smallmatrix})\) integers with the property that every \(k\)-subset of \([n]\) appears exactly \(t\)-times consecutively in the sequence. The author investigates the minimal number \(t= U(n, k)\) for which there is a \(t\)-cover Ucycle. For example: (a) \(U(n, 4)\leq 2\) if \(n\equiv 2\pmod 4\). (b) \(U(n,5)\leq 2\) if \(n\geq 16\) is relatively prime to 5 and \(n\not\equiv 2\pmod 3\).
scientific article; zbMATH DE number 719463