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Smallest Parts in Compositions

  • Arnold Knopfmacher
  • Augustine O. Munagi
Conference paper

Abstract

By analogy with recent Work of Andrews on smallest parts in partitions of integers, we consider smallest parts in compositions (ordered partitions) of integers. In particular, we study the number of smallest parts and the sum of smallest parts in compositions of n as well as the position of the first smallest part in a random composition of n.

Keywords

Asymptotic Estimate Geometric Distribution Integer Sequence Dominant Pole Part Size 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    G. E. Andrews, The Theory of Partitions, Addison-Wesley Publishing Co. (1976).Google Scholar
  2. 2.
    G. E. Andrews, The number of smallest parts in the partitions of n, J. Reine Angew. Math. 624 (2008), 133–142.Google Scholar
  3. 3.
    S. Corteel, C. Savage and H. Wilf, A note on partitions and compositions defined by inequalities, Integers 5 (2005), A24.Google Scholar
  4. 4.
    P. Flajolet and R. Sedgewick, Analytic Combinatorics, Cambridge University Press (2009).Google Scholar
  5. 5.
    C. Savage and H. Wilf, Pattern avoidance in compositions and multiset permutations, Adv. Appl. Math. 36 (2006), 194–201.Google Scholar
  6. 6.
    N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences, (available via: http://www.research.att.com/~njas/sequences/).
  7. 7.
    H. Wilf, generatingfunctionology, Academic Press Inc (1994).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.University of the WitwatersrandJohannesburgSouth Africa

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