# Math major Liem Nguyen wins Celebration of Scholarship Undergraduate School Award

Parity of K-regular Partition Functions.

A partition of a positive integer n is a non-increasing sequence of positive integers whose sum is n. A k-regular partition of a positive integer n is a partition of n whose parts are not divisible by k, and we denote bk(n) as the number of k-regular partitions of n. We are interested in the parity of these functions, in particular the exact criteria for when bk(n) is even. In this presentation, we will give such criteria for b7(n) and b13(n), and prove that these functions satisfy Ramanujan type congruences modulo 2.