Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
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Turkish Journal of Analysis and Number Theory. 2014, 2(4), 125-129
DOI: 10.12691/tjant-2-4-4
Open AccessArticle

Generating Function for M(m,n)

Sabuj Das1 and Haradhan Kumar Mohajan2,

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

2Premier University, Chittagong, Bangladesh

Pub. Date: July 31, 2014

Cite this paper:
Sabuj Das and 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

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.”

Keywords:
crank j-times vector partitions weight exponent

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References:

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[3]  Atkin, A.O.L. and Swinnerton-Dyer, P., Some Properties of Partitions, Proc. London Math. Soc. 3(4): 84-106. 1954.
 
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