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The Ramanujan Journal

, Volume 27, Issue 2, pp 163–167 | Cite as

A bijection for partitions with initial repetitions

  • William J. KeithEmail author
Article

Abstract

A theorem of Andrews equates partitions in which no part is repeated more than 2k−1 times to partitions in which, if j appears at least k times, all parts less than j also do so. This paper proves the theorem bijectively, with some of the generalizations that usually arise from such proofs.

Keywords

Partitions Initial k-repetitions 

Mathematics Subject Classification (2000)

05A17 11P81 

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References

  1. 1.
    Andrews, G.: Partitions with initial repetitions. Acta Math. Sin. Engl. Ser. 25(9), 1437–1442 (2009). doi: 10.1007/s10114-009-6292-y MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Andrews, G.: The Theory of Partitions. The Encyclopedia of Mathematics and Its Applications Series. Addison-Wesley, New York (1976), 300 pp. Reissued, Cambridge University Press, New York (1998) zbMATHGoogle Scholar
  3. 3.
    Stockhofe, D.: Bijektive Abbildungen auf der Menge der Partitionen einer Naturlichen Zahl. Bayreuth. Math. Schr. 10, 1–59 (1982) MathSciNetGoogle Scholar
  4. 4.
    Keith, W.: Ranks of Partitions and Durfee Symbols. Ph.D. Thesis, Pennsylvania State University (June 2007). URL: http://etda.libraries.psu.edu/theses/approved/WorldWideIndex/ETD-2026/index.html

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.University of LisbonLisbonPortugal

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