DEVELOPMENT OF FOKKINK-FOKKINK-WANG’S GENERATING FUNCTION FOR FFW(n)
DOI:
https://doi.org/10.29121/granthaalayah.v3.i2.2015.3041Keywords:
Distinct Parts, FFW-Function, Positive Divisors, Smallest Part, Spt-Function, Spt-CrankAbstract [English]
In 1995, R. Fokkink, W. Fokkink and Wang defined the in terms of , where is the smallest part of partition . In 2008, Andrews obtained the generating function for . In 2013, Andrews, Garvan and Liang extended the FFW-function and obtained the similar expressions for the spt-function and then defined the spt-crank generating functions. They also defined the generating function for in various ways. This paper shows how to find the number of partitions of n into distinct parts with certain conditions and shows how to prove the Theorem 1 by induction method. This paper shows how to prove the Theorem 2 with the help of two generating functions.
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References
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