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Generating Functions for P1r (n) and P2r (n)

Author

Listed:
  • Das, Sabuj
  • Mohajan, Haradhan

Abstract

In 1970 George E. Andrews defined the generating functions for P1r (n) and P2r (n). In this article these generating functions are discussed elaborately. This paper shows how to prove the theorem P2r (n) = P3r (n) with a numerical example when n = 9 and r = 2. In 1966 Andrews defined the terms A/(n) and B/(n), but this paper proves the remark A/(n) = B/(n) with the help of an example when n = 10. In 1961, N. Bourbaki defined the term P(n, m). This paper shows how to prove a Remark in terms of P(n, m), where P(n, m) is the number of partitions of the type of enumerated by P3r (n ) with the further restrictions that b1

Suggested Citation

  • Das, Sabuj & Mohajan, Haradhan, 2014. "Generating Functions for P1r (n) and P2r (n)," MPRA Paper 83698, University Library of Munich, Germany, revised 30 May 2014.
    • Handle: RePEc:pra:mprapa:83698
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    Citations

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    Cited by:

    1. Mohajan, Devajit & Mohajan, Haradhan, 2023. "The Responses of an Organization for the Increase in Wage Rates: Profit Maximization Cases," MPRA Paper 118238, University Library of Munich, Germany, revised 10 Jun 2023.
    2. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Broca Index: A Simple Tool to Measure Ideal Body Weight," MPRA Paper 116852, University Library of Munich, Germany, revised 18 Jan 2023.
    3. Mohajan, Devajit & Mohajan, Haradhan, 2023. "An Economical Study When Cost of Irregular Raw Materials of an Industry Increases for Nonlinear Budget Constraint," MPRA Paper 118176, University Library of Munich, Germany, revised 05 May 2023.

    More about this item

    Keywords

    Generating functions; number of partitions.;

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables

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