On the number of partitions of n into k different parts

Byungchan Kim

doi:10.1016/j.jnt.2012.01.003

On the number of partitions of n into k different parts

Byungchan Kim

School of Natural Sciences

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

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.

Original language	English
Pages (from-to)	1306-1313
Number of pages	8
Journal	Journal of Number Theory
Volume	132
Issue number	6
DOIs	https://doi.org/10.1016/j.jnt.2012.01.003
State	Published - Jun 2012

Keywords

Divisor function
Overpartitions
Restricted integer partitions

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10.1016/j.jnt.2012.01.003

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AB - 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.

KW - Divisor function

KW - Overpartitions

KW - Restricted integer partitions

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JO - Journal of Number Theory

JF - Journal of Number Theory

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On the number of partitions of n into k different parts

Abstract

Keywords

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