Skip to main content
SpringerLink
Log in

On the compositions of an integer

  • Contributed Papers
  • Conference paper
  • First Online:
Combinatorial Mathematics VII

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 829))

Abstract

We prove that for all positive integers n, the number of compositions of n in which the largest part is m is a unimodal function of m.

B. Richmond’s research was supported by NRC Grant No. A4067.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G.E. Andrews, A theorem on reciprocal polynomials with applications to permutations and compositions, Amer. Math. Monthly 82 (1975), 830–833.

    Article  MathSciNet  MATH  Google Scholar 

  2. N. Basu, A note on partitions, Bull. Calcutta Math. Soc. 44 (1952), 27–30.

    MathSciNet  MATH  Google Scholar 

  3. E.N. Gilbert, Synchronization of binary messages, IRE Trans. Inform. Theory IT-6 (1960), 470–477.

    Article  MathSciNet  Google Scholar 

  4. L.J. Guibas and A.M. Odlyzko, Long repetitive patterns in random sequences, (to appear).

    Google Scholar 

  5. P.A. MacMahon, Memoir on the theory of the compositions of numbers, Philos. Trans. Roy. Soc. London Ser. A 184 (1890), 835–901.

    Article  MATH  Google Scholar 

  6. A. Robins, A remark on Stirling’s formula, Amer. Math. Monthly 62 (1955), 26–29.

    Article  MathSciNet  Google Scholar 

  7. Z. Star, An asymptotic formula in the theory of compositions, Aequationes Math. 13 (1976), 279–284.

    Article  MathSciNet  MATH  Google Scholar 

  8. E.T. Whittaker and G.N. Watson, A Course of Modern Analysis. 4th ed. (Cambridge Univ. Press, Cambridge, 1927).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Bell Laboratories, Murray Hill, New Jersey, U.S.A.

    A. Odlyzko & B. Richmond

  2. Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, Canada

    A. Odlyzko & B. Richmond

Authors
  1. A. Odlyzko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. Richmond
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Robert W. Robinson George W. Southern Walter D. Wallis

Rights and permissions

Reprints and permissions

Copyright information

© 1980 Springer-Verlag

About this paper

Cite this paper

Odlyzko, A., Richmond, B. (1980). On the compositions of an integer. In: Robinson, R.W., Southern, G.W., Wallis, W.D. (eds) Combinatorial Mathematics VII. Lecture Notes in Mathematics, vol 829. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088913

Download citation

  • DOI: https://doi.org/10.1007/BFb0088913

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10254-0

  • Online ISBN: 978-3-540-38376-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation