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M. Merca. A note on the partitions involving parts of k different magnitudes. Journal of Number Theory, 162, pp. 23-34, 2016.

Abstract: The natural expression of the generating function N_k(q)for the number of partitions of the positive integer nthat have exactly kdistinct values for the parts was remarked by MacMahon. A factorization of this generating function was derived later by Andrews. In this paper, the author considers a truncated form of N_k(q)to give a new proof of Andrews's identity. A generalization of a recent connection between partitions and divisors is presented in this context.

Keywords: Partitions, Divisors

URL: http://dx.doi.org/10.1016/j.jnt.2015.10.021

Posted by Mircea Merca

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