On the distribution of a restricted parity excess

Abstract

Let (pe) over tilde(lambda) be the restricted parity excess, which is the number of different odd parts minus the number of different even parts in the partition lambda. We define a random variable X-n which takes value (pe) over tilde(lambda) while we choose lambda uniformly at random from the set of partitions of n. Then, we show that X-n is asymptotically normally distributed.