Science and Education Publishing
Turkish Journal of Analysis and Number Theory
2
4
2014
07
31
Generating Function for M(m,n)
125
129
EN
Sabuj
Das
Haradhan Kumar
Mohajan
Premier University, Chittagong, Bangladesh
TJANT2014244
10.12691/tjant-2-4-4
2014
04
04
2014
04
14
2014
07
31
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 of n with crank C()=m is M(m,n) for all n>1."