Drexel University Home Pagewww.drexel.edu DREXEL UNIVERSITY LIBRARIES HOMEPAGE >>
iDEA DREXEL ARCHIVES >>

iDEA: Drexel E-repository and Archives > Drexel Academic Community > College of Arts and Sciences > Department of Mathematics > Faculty Research and Publications (Mathematics) > A local limit theorem in the theory of overpartitions

Please use this identifier to cite or link to this item: http://hdl.handle.net/1860/1634

Title: A local limit theorem in the theory of overpartitions
Authors: Corteel, Sylvie
Goh, William M.Y.
Hitczenko, Pawel
Keywords: Partitions;Combinatorial probability;Local limit theorem;Asymptotic analysis
Issue Date: 2006
Publisher: Springer Verlag
Citation: Algorithmica, 46(3-4): pp. 329-343.
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 ! 1 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 ± k for k = o(n) and the probability that the weight of the overlined parts counted with multiplicity is n/2 ± k for k = o(n). The first computation is straightforward and uses known asymptotics of partitions. The second one is more involved and requires a sieve argument and the application of the saddle point method. From that we can directly evaluate the probability that two random partitions of n do not share a part.
URI: http://www.doi.org/10.1007/s00453-006-0102-z
http://hdl.handle.net/1860/1634
Appears in Collections:Faculty Research and Publications (Mathematics)

Files in This Item:

File Description SizeFormat
2006175069.pdf247.7 kBAdobe PDFView/Open
View Statistics

Items in iDEA are protected by copyright, with all rights reserved, unless otherwise indicated.

 

Valid XHTML 1.0! iDEA Software Copyright © 2002-2010  Duraspace - Feedback