On the number of segregating sites

Understand

Consider a sample of size n drawn from a large, neutral population of haploid individuals subject to mutation whose genealogy is governed by Kingmans n-coalescent.

• Let Sn count the number of segregating sites in this sample under the infinitely many sites model of Kimura.
• For fixed sample size n the main result about Sn is due to Watterson who computed its mean and variance.
• In our main result, Theorem 3, we generalize Watterson's result and compute the ith cumulant of Sn.