IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/83044.html
   My bibliography  Save this paper

Bingmann-Lovejoy-Osburn’s generating function in the overpartitions

Author

Listed:
  • Hossain, Fazlee
  • Das, Sabuj
  • Mohajan, Haradhan

Abstract

In 2009, Bingmann, Lovejoy and Osburn defined the generating function for spt(n). In 2012, Andrews, Garvan and Liang defined the sptcrank in terms of partition pairs. In this article the number of smallest parts in the overpartitions of n with smallest part not overlined is discussed, and the vector partitions and S ̅ -partitions with 4 components, each a partition with certain restrictions are also discussed. The generating function for spt(n), and the generating function for Ms(m, n) are shown with a result in terms of modulo 3. This paper shows how to prove the Theorem 1 in terms of Ms(m, n) with a numerical example, and shows how to prove the Theorem 2 with the help of sptcrank in terms of partition pairs. In 2014, Garvan and Jennings-Shaffer are able to define the sptcrank for marked overpartitions. This paper also shows another result with the help of 6 SP -partition pairs of 3 and shows how to prove the Corollary with the help of 42 marked overpartitions of 6.

Suggested Citation

  • Hossain, Fazlee & Das, Sabuj & Mohajan, Haradhan, 2014. "Bingmann-Lovejoy-Osburn’s generating function in the overpartitions," MPRA Paper 83044, University Library of Munich, Germany, revised 01 Aug 2014.
    • Handle: RePEc:pra:mprapa:83044
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/83044/1/MPRA_paper_83044.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Economic Aspects of Profit Maximization if Cost of Principal Raw Material Increases," MPRA Paper 117453, University Library of Munich, Germany, revised 22 Mar 2023.
    2. Mohajan, Devajit, 2023. "Mathematical Analysis of an Industry When Cost of Principal Raw Materials Increase: A Nonlinear Budget Constraint Attempt," MPRA Paper 118933, University Library of Munich, Germany.

    More about this item

    Keywords

    Components; Congruent; Crank; Non-Negative; Overpartitions; Overlined; Weight;
    All these keywords.

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:83044. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.