# Seminars & Colloquia Calendar

Number Theory Seminar

## Partitions into powers of primes

#### Ayla Gafini, University of Mississippi

Location:  URL: https://us02web.zoom.us/j/386354493?pwd=WEZLaXdSV20vNFpMVVRpb0xXWGhBZz09
Date & time: Tuesday, 14 April 2020 at 2:00PM - 3:00PM

Abstract: 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 $$p_{\mathcal P_k}(n)$$ where $$\mathcal P_k$$ is the set of $$k$$-th powers of primes.  Powers of primes are both sparse and irregular, which makes $$p_{\mathcal P_k}(n)$$ 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.

Meeting ID: 386 354 493