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Multiplicity and Number of Parts in Overpartitions
Sylvie Corteel1 and Pawel Hitczenko2
1Chargée de Recherche CNRS affectée au PRiSM, Université de Versailles, Versailles, France
2Department of Mathematics and Computer Science, Drexel University, Philadelpia, USA
Annals of Combinatorics 8 (3) p.287-301 September, 2004
AMS Subject Classification:05A17, 60C05, 11P82
The purpose of this paper is to study the parts, part sizes and multiplicities in overpartitions using combinatorics, probabilities and asymptotics. We show that the probability that a randomly chosen part size of a randomly chosen overpartition of n has multiplicity m or m+1 approaches 1/(m(m+1)ln 2) and that the expected multiplicity of a randomly chosen part size of a randomly chosen overpartition of n approaches lnn/(4ln2) as n
Keywords: partitions, combinatorial probability


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