Confirming the Kleitman-Winston conjecture on the largest coefficient in aq-Catalan number

Authors
Kim, JH Pittel, B
Citation
Jh. Kim et B. Pittel, Confirming the Kleitman-Winston conjecture on the largest coefficient in aq-Catalan number, J COMB TH A, 92(2), 2000, pp. 197-206
Citations number
8
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF COMBINATORIAL THEORY SERIES A
ISSN journal
00973165 → ACNP
Volume
92
Issue
2
Year of publication
2000
Pages
197 - 206
Database
ISI
SICI code
0097-3165(200011)92:2<197:CTKCOT>2.0.ZU;2-Y
Abstract
In 1983 Kleitman and Winston conjectured that the largest coefficient in an nth q-Catalan number is of order O(4(n)/n(3/2)). Assuming its truth, they proved that the total number of n-tournament score sequences is O(4(n)/n(5/ 2)), thus matching their own lower bound. Our purpose is to confirm the con jecture. (C) 2000 Academic Press.