eng
Science and Education Publishing
Turkish Journal of Analysis and Number Theory
2014-07-31
2
4
125
129
10.12691/tjant-2-4-4
TJANT2014244
article
Generating Function for M(m,n)
Sabuj Das
1
Haradhan Kumar Mohajan
2
Senior Lecturer, Department of Mathematics, Raozan University College, Bangladesh
Premier University, Chittagong, Bangladesh
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."
http://pubs.sciepub.com/tjant/2/4/4/tjant-2-4-4.pdf
crank
j-times
vector partitions
weight
exponent