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 PublishingCite 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.comAbstract
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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