Mohajan, Haradhan
(2014):
*Generating Function for M(m, n).*
Published in: Turkish Journal of Analysis and Number Theory
, Vol. 2, No. 4
(31 July 2014): pp. 125-129.

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## 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.”

Item Type: | MPRA Paper |
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Original Title: | Generating Function for M(m, n) |

English Title: | Generating Function for M(m, n) |

Language: | English |

Keywords: | Crank, j-times, vector partitions, weight, exponent |

Subjects: | C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C65 - Miscellaneous Mathematical Tools |

Item ID: | 83594 |

Depositing User: | Haradhan Kumar Mohajan |

Date Deposited: | 03 Jan 2018 16:31 |

Last Modified: | 01 Oct 2019 18:18 |

References: | [1] Andrews, G.E., The Theory of Partitions, Encyclopedia of Mathematics and its Application, vol. 2 (G-c, Rotaed) Addison-Wesley, Reading, mass, 1976 (Reissued, Cambridge University, Press, London and New York 1985). 1985. [2] Andrews, G.E. and Garvan, F.G., Dyson’s Crank of a Partition, Bulletin (New series) of the American Mathematical Society, 18(2): 167–171. 1988. [3] Atkin, A.O.L. and Swinnerton-Dyer, P., Some Properties of Partitions, Proc. London Math. Soc. 3(4): 84–106. 1954. [4] Garvan, F.G., Ramanujan Revisited, Proceeding of the Centenary Conference, University of Illinois, Urban-Champion. 1988. [5] Garvan, F.G.. Dyson’s Rank Function and Andrews’ spt-function, University of Florida, Seminar Paper Presented in the University of Newcastle on 20 August 2013. 2013. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/83594 |