aequationes mathematicae

, Volume 49, Issue 1, pp 86–97 | Cite as

Compositions with distinct parts

  • B. Richmond
  • A. Knopfmacher
Research Papers

Abstract

The number of compositionsC(n) of a positive integern into distinct parts can be considered as a natural analogue of the numberq(n) of distinct partitions ofn. We obtain an asymptotic estimate forC(n) and in addition show that the sequence {C(n, k)} of distinct compositions ofn withk distinct parts is unimodal. Our analysis is more complicated than is usual for composition problems. The results imply however that the behaviour of these functions is of comparable complexity to partition problems.

AMS (1991) subject classification

11P82 

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Copyright information

© Birkhäuser Verlag 1995

Authors and Affiliations

  • B. Richmond
    • 1
    • 2
  • A. Knopfmacher
    • 1
    • 2
  1. 1.Dept. of Combinatorics & OptimizationUniversity of WaterlooWaterlooCanada
  2. 2.Dept. of Computational & Applied MathematicsUniversity of the WitwatersrandJohannesburgSouth Africa

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