✦ LIBER ✦

Confirming the Kleitman–Winston Conjecture on the Largest Coefficient in a q-Catalan Number

✍ Scribed by Jeong Han Kim; Boris Pittel

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 114 KB
Volume: 92
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.1999.3054

No coin nor oath required. For personal study only.

✦ Synopsis

In 1983 Kleitman and Winston conjectured that the largest coefficient in an n th q-Catalan number is of order O(4 n Ân 3Â2 ). Assuming its truth, they proved that the total number of n-tournament score sequences is O(4 n Ân 5Â2 ), thus matching their own lower bound. Our purpose is to confirm the conjecture.