On the number of partitions of n into k different parts |
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| Authors: | Byungchan Kim |
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| Institution: | School of Liberal Arts and Institute for Convergence Fundamental Studies, Seoul National University of Science and Technology, 172 Gongreung 2 dong, Nowongu, Seoul, 139-743, Republic of Korea |
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| Abstract: | We study the number of partitions of n into k different parts by constructing a generating function. As an application, we will prove mysterious identities involving convolution of divisor functions and a sum over partitions. By using a congruence property of the overpartition function, we investigate values of a certain convolution sum of two divisor functions modulo 8. |
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