Confirming the Kleitman-Winston conjecture on the largest coefficient in a \(q\)-Catalan number
type: Item
instance of: scholarly article
title: Confirming the Kleitman-Winston conjecture on the largest coefficient in a \(q\)-Catalan number
zbMATH Open document ID: 0968.05037
author: Jeong Han Kim
author: Boris Pittel
published in: Journal of Combinatorial Theory. Series A
publication date: 2001-02-22T00:00:00Z
review text: 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 \(O(4^n/n^{5/2})\).
Mathematics Subject Classification ID: 05C20
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 60C05
zbMATH DE Number: 1569474
zbMATH Keywords: \(q\)-Catalan number
zbMATH Keywords: tournament score sequences
reviewed by: J. W. Moon
MaRDI profile type: Publication
full work available at URL: jcta.1999.3054
OpenAlex ID: W2067555633
Wikidata QID: Q123028239
cites work: Central and local limit theorems for the coefficients of polynomials of binomial type
cites work: Q3999383
cites work: Q5514188
cites work: On the asymptotic number of tournament score sequences
cites work: Q5585195
cites work: Q5646918
cites work: A bernoulli excursion and its various applications
DOI: 10.1006/JCTA.1999.3054
description: scientific article; zbMATH DE number 1569474