Generating Function for M(m,n)

Sabuj Das¹ and Haradhan Kumar Mohajan^2,

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

²Premier University, Chittagong, Bangladesh

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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