Tutte seminar - Bruce Richmond

Friday, May 30, 2008 3:30 pm - 4:30 pm EDT (GMT -04:00)

On the Maximum of the Stirling Numbers

Speaker: Bruce Richmond
Affiliation: University of Waterloo
Room: Mathematics & Computer Building (MC) 5158


Say an integer n is exceptional if the maximum Stirling number of the second kind S(n, k) occurs for two(of necessity consecutive) values of k. We with Graeme Kemkes and Donatella Merlini have shown that the number of exceptional integers less than or equal to x is O(x^{1/2+\e}) for any \e > 0. We derive a similar result for partitions of n into exactly k parts p(n, k). The estimates of Bombieri and Pila for lattice points on convex curves and the asymptotic behaviour of S(n, k) and p(n, k) are required.