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Analysis of some new partition statistics

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Abstract

We study several statistics for integer partitions: for a random partition of an integer n we consider the average size of the smallest gap (missing part size), the multiplicity of the largest part, and the largest repeated part size. Furthermore, we estimate the number of gap-free partitions of n.

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Authors and Affiliations

  1. Institut für Mathematik A, Technische Universität Graz, Steyrergasse 30, 8010, Graz, Austria

    Peter J. Grabner

  2. The John Knopfmacher Centre for Applicable Analysis and Number Theory, Department of Mathematics, University of the Witwatersrand, P. O. Wits, 2050, Johannesburg, South Africa

    Arnold Knopfmacher

Authors
  1. Peter J. Grabner
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  2. Arnold Knopfmacher
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Correspondence to Peter J. Grabner.

Additional information

2000 Mathematics Subject Classification Primary—05A17; Secondary—11P82

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Grabner, P.J., Knopfmacher, A. Analysis of some new partition statistics. Ramanujan J 12, 439–454 (2006). https://doi.org/10.1007/s11139-006-0153-4

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  • DOI: https://doi.org/10.1007/s11139-006-0153-4

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