Partition polynomials: asymptotics and zeros (original) (raw)

2007

Abstract

Abstract: Let $ F_n (x) $ be the partition polynomial sumk=1npk(n)xk\ sum_ {k= 1}^ n p_k (n) x^ k sumk=1npk(n)xk where $ p_k (n) $ is the number of partitions of $ n $ with $ k $ parts. We emphasize the computational experiments using degrees up to 70,00070,000 70,000 to discover the asymptotics of these polynomials. Surprisingly, the asymptotics of $ F_n (x) $ have two scales of orders $ n $ and sqrtn\ sqrt {n} sqrtn and in three different regimes inside the unit disk. Consequently, the zeros converge to network of curves inside the unit disk given in terms of the dilogarithm.

Robert Boyer hasn't uploaded this paper.

Let Robert know you want this paper to be uploaded.

Ask for this paper to be uploaded.