## – Europe/Lisbon

Room P3.10, Mathematics Building
— Online

Jonathan Bradley-Thrush, Instituto Superior Técnico (GFM), Universidade de Lisboa

Ferrers diagrams and *q*-series identities

A Ferrers diagram is a graphical way of representing an integer partition. A *q*-series is a series in which the ratio of the *n*th term to the next is a rational function of *q ^{n}*. With reference to the origins of the subject in the work of Sylvester, I will present a short introduction to the use of Ferrers diagrams in giving combinatorial interpretations of

*q*-series identities. I will then move on to more recent developments involving a sort of generalized partition, called an overpartition. Finally, I will describe some further generalizations and related open problems.