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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.

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Article

Generating Function for M(m,n)

1Senior Lecturer, Department of Mathematics, Raozan University College, Bangladesh

2Premier University, Chittagong, Bangladesh


Turkish Journal of Analysis and Number Theory. 2014, Vol. 2 No. 4, 125-129
DOI: 10.12691/tjant-2-4-4
Copyright © 2014 Science and Education Publishing

Cite this paper:
Sabuj Das, Haradhan Kumar Mohajan. Generating Function for M(m,n). Turkish Journal of Analysis and Number Theory. 2014; 2(4):125-129. doi: 10.12691/tjant-2-4-4.

Correspondence to: Haradhan  Kumar Mohajan, Premier University, Chittagong, Bangladesh. Email: haradhan_km@yahoo.com

Abstract

This paper shows that the coefficient of x in the right hand side of the equation 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.”

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