@article{tjant2014244,
author={{Das, Sabuj and Mohajan, Haradhan Kumar},
title={Generating Function for M(m,n)},
journal={Turkish Journal of Analysis and Number Theory},
volume={2},
number={4},
pages={125--129},
year={2014},
url={http://pubs.sciepub.com/tjant/2/4/4},
abstract={This paper shows that the coefficient of <i>x</i> in the right hand side of the equation <img src=image/abs1.png></img> is an algebraic relation in terms of <i>z</i>. The exponent of <i>z</i> represents the crank of partitions of a positive integral value of <i>n</i> and also shows that the sum of weights of corresponding partitions of <i>n</i> is the sum of ordinary partitions of <i>n</i> and it is equal to the number of partitions of <i>n</i> with crank <i>m</i>. This paper shows how to prove the Theorem ¡°The number of partitions <span style="font-family:Times New Roman; font-size:16px;">&#960;</span> of <i>n</i> with crank C(<span style="font-family:Times New Roman; font-size:16px;">&#960;</span>)=m is M(m,n) for all n>1.¡±},
doi={10.12691/tjant-2-4-4}
publisher={Science and Education Publishing}
}