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arXiv · 1809.07459

Parity of the Partition Function p(n,k)

Kedar Karhadkar
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Abstract

Let p(n, k) denote the number of partitions of n into parts less than or equal to k. We show several properties of this function modulo 2. First, we prove that for fixed positive integers k and m, p(n,k) is periodic modulo m. Using this, we are able to find lower and upper bounds for the number of odd values of the function for a fixed k.

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Kedar Karhadkar. 2018-11-20. Parity of the Partition Function p(n,k). https://arxiv.org/abs/1809.07459

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