A Local Limit Theorem in the Theory of Overpartitions

Abstract. An overpartition of an integer n is a partition where the last occurrence of a part can be overlined. We study the weight of the overlined parts of an overpartition counted with or without their multiplicities. This is a continuation of a work by Corteel and Hitczenko where it was shown that the expected weight of the overlined parts is asymptotic to n/3 as n and that the expected weight of the of the overlined parts counted with multiplicity is n/2. Here we refine these results. We first compute the asymptotics of the variance of the weight of the overlined parts counted with multiplicity. We then asymptotically evaluate the probability that the weight of the overlined parts is n/3

• Type: Journal
• Year: 2006
• Where: ALGORITHMICA
• Authors: Sylvie Corteel, William M. Y. Goh, Pawel Hitczenko
• Keywords: ALGORITHMICA 2006, Asymptotics, Integer, Overlined Parts