Emily Sergel, University of Pennsylvania

Abstract

 An s,t-core partition is a partition with no hook length equal to s or t. Recently Ekhad-Zeilberger used experimental methods to prove that the asymptotic distribution size among s,t-cores (with s-t fixed) is not normal. Following that, Zaleski gave strong evidence that (s,s+1)-cores with distinct parts are asymptotically normally distributed. My coauthors and I found both results surprising, and the proof we discovered for the later one uses some beautiful, classical results. The main purpose of this talk is to spread these tools. If time permits, I will also discuss the possibility (and challenge) of applying these tools to related core problems. Joint work with János Komlós and Gábor Tusnády.