Confirming the Kleitman-Winston conjecture on the largest coefficient in a \(q\)-Catalan number
The authors prove a conjecture of \textit{K. J. Winston} and \textit{D. J. Kleitman} [J. Comb. Theory, Ser. A 35, 208-230 (1983; Zbl 0513.05029)] that the largest coefficient in an \(n\)th order \(q\)-Catalan number is of order \(O(4^n/n^3)\). From this it follows, as Kleitman and Winston showed, that the number of non-decreasing tournament score sequences of length \(n\) is of order \(O(4^n/n^{5/2})\).
scientific article; zbMATH DE number 1569474