An Identity for the Partition Function Involving Parts of k Different Magnitudes

Saud Hussein

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arXiv · 1806.05416

An Identity for the Partition Function Involving Parts of k Different Magnitudes

Saud Hussein

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Abstract

Using previous work by Merca, we show the partition function involving parts of k different magnitudes, shifted by the triangular numbers, equals the self convolution of the unrestricted partition function. We also provide a combinatorial proof of this result.

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Saud Hussein. 2018-06-14. An Identity for the Partition Function Involving Parts of k Different Magnitudes. https://arxiv.org/abs/1806.05416

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