Limit distributions of smallest gap and largest repeated part in integer partitions
Date
2011
Authors
Wagner S.
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Abstract
We study two parameters in random integer partitions, namely the first gap and the last repeated part, that have been introduced by Grabner and Knopfmacher in a recent paper (Ramanujan J. 12(3):439-454, 2006). More generally, the first part that occurs at most r times and the last part that occurs at least r times are considered. For both parameters, we determine the limit distribution, which turn out to be the Rayleigh and Gumbel distributions, respectively. This also generalises the well-known result by Erdo{double acute}s and Lehner on the distribution of the largest part in a random integer partition. Furthermore, extensions to general Λ-partitions and results on related parameters, such as the length of the first gap, are provided. © 2011 Springer Science+Business Media, LLC.
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Ramanujan Journal
25
2
229
246
25
2
229
246