An almost-bijective proof of an asymptotic property of partitions†

  1. Aaron D. Jaggard‡,*

Article first published online: 7 JUN 2007

DOI: 10.1002/rsa.20180

Issue

Random Structures & Algorithms

Random Structures & Algorithms

Volume 31, Issue 2, pages 247–250, September 2007

Additional Information

How to Cite

Jaggard, A. D. (2007), An almost-bijective proof of an asymptotic property of partitions. Random Structures & Algorithms, 31: 247–250. doi: 10.1002/rsa.20180

Author Information

  1. Department of Mathematics, Tulane University, New Orleans, Louisiana 70118

  1. ‡

    Partially supported by NSF grant DMS 0239996.

*Department of Mathematics, Tulane University, New Orleans, Louisiana 70118

  1. †

    Part of this work was carried out when the author was at the University of Pennsylvania.

Publication History

  1. Issue published online: 24 JUL 2007
  2. Article first published online: 7 JUN 2007
  3. Manuscript Accepted: 18 JUL 2006
  4. Manuscript Received: 30 OCT 2005

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Keywords:

  • integer partition;
  • part multiplicity;
  • asymptotic probability

Abstract

Let ��n be the set of all distinct ordered pairs (λ,λi), where λ is a partition of n and λi is a part size of λ. The primary result of this note is a combinatorial proof that the probability that, for a pair (λ,λi) chosen uniformly at random from ��n, the multiplicity of λi in λ is 1 tends to 1/2 as n →∞. This is inspired by work of Corteel, Pittel, Savage, and Wilf (Random Structures and Algorithms 14 (1999), 185–197). © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007

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