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Generating Function for M(m, n)

Author

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  • Mohajan, Haradhan

Abstract

This paper shows that the coefficient of x in the right hand side of the equation for M(m, n) for all n >1 is an algebraic relation in terms of z. The exponent of z represents the crank of partitions of a positive integral value of n and also shows that the sum of weights of corresponding partitions of n is the sum of ordinary partitions of n and it is equal to the number of partitions of n with crank m. This paper shows how to prove the Theorem “The number of partitions π of n with crank C(π) = m is M(m, n) for all n >1.”

Suggested Citation

  • Mohajan, Haradhan, 2014. "Generating Function for M(m, n)," MPRA Paper 83594, University Library of Munich, Germany, revised 14 Apr 2014.
    • Handle: RePEc:pra:mprapa:83594
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    File URL: https://mpra.ub.uni-muenchen.de/83594/1/MPRA_paper_83594.pdf
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    Citations

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    Cited by:

    1. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Various Problems Arise in Industrial Economics If Wage Rate Increases: A Study for Nonlinear Budget Constraint," MPRA Paper 117553, University Library of Munich, Germany, revised 04 Apr 2023.
    2. 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.
    3. 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.
    4. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Effects of Various Inputs for Increased Interest Rate of Capital: A Nonlinear Budget Constraint Consideration," MPRA Paper 118134, University Library of Munich, Germany, revised 06 May 2023.
    5. 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.
    6. 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.
    7. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Economic Investigation of Lagrange Multiplier if Cost of Inputs and Budget Size of a Firm Increase: A Profit Maximization Endeavor," MPRA Paper 117993, University Library of Munich, Germany, revised 07 May 2023.

    More about this item

    Keywords

    Crank; j-times; vector partitions; weight; exponent;
    All these keywords.

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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