IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/83049.html
   My bibliography  Save this paper

Generalization of Euler and Ramanujan’s Partition Function

Author

Listed:
  • Mohajan, Haradhan

Abstract

The theory of partitions has interested some of the best minds since the 18th century. In 1742, Leonhard Euler established the generating function of P(n). Godfrey Harold Hardy said that Srinivasa Ramanujan was the first, and up to now the only, mathematician to discover any such properties of P(n). In 1981, S. Barnard and J.M. Child stated that the different types of partitions of n in symbolic form. In this paper, different types of partitions of n are also explained with symbolic form. In 1952, E. Grosswald quoted that the linear Diophantine equation has distinct solutions; the set of solution is the number of partitions of n. This paper proves theorem 1 with the help of certain restrictions. In 1965, Godfrey Harold Hardy and E. M. Wright stated that the ‘Convergence Theorem’ converges inside the unit circle. Theorem 2 has been proved here with easier mathematical calculations. In 1853, British mathematician Norman Macleod Ferrers explained a partition graphically by an array of dots or nodes. In this paper, graphic representation of partitions, conjugate partitions and self-conjugate partitions are described with the help of examples.

Suggested Citation

  • Mohajan, Haradhan, 2015. "Generalization of Euler and Ramanujan’s Partition Function," MPRA Paper 83049, University Library of Munich, Germany, revised 06 Nov 2015.
    • Handle: RePEc:pra:mprapa:83049
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/83049/1/MPRA_paper_83049.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Das, Sabuj & Mohajan, Haradhan, 2014. "Generating Functions for and," MPRA Paper 55684, University Library of Munich, Germany, revised 22 Jan 2014.
    2. Das, Sabuj & Mohajan, Haradhan, 2014. "The Number of Vector Partitions of n with the Crank m," MPRA Paper 83697, University Library of Munich, Germany, revised 18 Aug 2014.
    Full references (including those not matched with items on IDEAS)

    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. "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. "Glaserian Grounded Theory and Straussian Grounded Theory: Two Standard Qualitative Research Approaches in Social Science," MPRA Paper 117017, University Library of Munich, Germany, revised 20 Feb 2023.
    3. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Mathematical Model for Nonlinear Budget Constraint: Economic Activities on Increased Budget," MPRA Paper 117299, University Library of Munich, Germany, revised 17 Mar 2023.
    4. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Long-Term Regular Exercise Increases V̇O2max for Cardiorespiratory Fitness," MPRA Paper 116962, University Library of Munich, Germany, revised 04 Feb 2023.
    5. Mohajan, Devajit & Mohajan, Haradhan, 2023. "A Study on Nonlinear Budget Constraint of a Local Industrial Firm of Bangladesh: A Profit Maximization Investigation," MPRA Paper 117324, University Library of Munich, Germany, revised 27 Mar 2023.
    6. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Sensitivity Analysis for Utility Maximization: A Study on Lagrange Multipliers and Commodity Coupons," MPRA Paper 117077, University Library of Munich, Germany, revised 06 Jan 2023.
    7. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Sensitivity Analysis of Inputs of an Organization: A Profit Maximization Exploration," MPRA Paper 117121, University Library of Munich, Germany, revised 12 Mar 2023.
    8. 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.
    9. Mohajan, Devajit & Mohajan, Haradhan, 2023. "A Study on Body Fat Percentage for Physical Fitness and Prevention of Obesity: A Two Compartment Model," MPRA Paper 117158, University Library of Munich, Germany, revised Feb 2023.
    10. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Bulimia Nervosa: A Psychiatric Problem of Disorder," MPRA Paper 117258, University Library of Munich, Germany, revised 17 Mar 2023.
    11. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Sensitivity Analysis between Lagrange Multipliers and Consumer Budget: Utility Maximization Case," MPRA Paper 116907, University Library of Munich, Germany, revised 19 Feb 2023.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sabuj, Das & Mohajan, Haradhan, 2014. "Development of Partition Functions of Ramanujan’s Works," MPRA Paper 83045, University Library of Munich, Germany, revised 15 Aug 2014.
    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. Hossain, Fazlee & Das, Sabuj, 2015. "The Rogers-Ramanujan Identities," MPRA Paper 83043, University Library of Munich, Germany, revised 28 Mar 2015.

    More about this item

    Keywords

    Ferrers and Young diagram; generating function; partitions; Ramanujan;
    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
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

    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:83049. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.