Generating Function for M(m, n)

Dr Haradhan Mohajan ()

MPRA Paper from University Library of Munich, Germany

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.”

Keywords: Crank; j-times; vector partitions; weight; exponent (search for similar items in EconPapers)
JEL-codes: C3 C65 (search for similar items in EconPapers)
Date: 2014-04-04, Revised 2014-04-14
References: View complete reference list from CitEc
Citations: View citations in EconPapers (7)

Published in Turkish Journal of Analysis and Number Theory 4.2(2014): pp. 125-129

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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:83594

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