Munich Personal RePEc Archive

Generating Function for M(m, n)

Mohajan, Haradhan (2014): Generating Function for M(m, n). Published in: Turkish Journal of Analysis and Number Theory , Vol. 2, No. 4 (31 July 2014): pp. 125-129.

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Abstract

This paper shows that the coefficient of x in the right hand side of the equation for M(m, n) for all n >1 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.”

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