Parity of the Partition Function p(n,k)
Combinatorics
2018-11-21 v2
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.
Cite
@article{arxiv.1809.07459,
title = {Parity of the Partition Function p(n,k)},
author = {Kedar Karhadkar},
journal= {arXiv preprint arXiv:1809.07459},
year = {2018}
}