Ayla Gafni

Asymptotics of Restricted Partition Functions - FRIDAY

Given a set $\mathcal A \subset \mathbb N$, the restricted partition function $p_{\mathcal{A}}(n)$ counts the number of integer partitions of $n$ with all parts in $\mathcal A$. In this talk, we will explore the features of the restricted partitions function $p_{\mathbb P_k}(n)$ where $\mathcal P_k$ is the set of $k$-th powers of primes. Powers of primes are both sparse and irregular, which makes $p_{\mathbb P_k}(n)$ quite an elusive function to understand. We will discuss some of the challenges involved in studying restricted partition functions and what is known in the case of primes, $k$-th powers, and $k$-th powers of primes.