ConferenceARTA III Advances in Representation Theory of Algebras
The third Advances in Representation Theory of Algebras (ARTA) meeting will be held at the Université du Québec à Montréal, Montréal, Québec, Canada, from the 16th to the 20th of June 2014.
There is a beautiful bijection (due to Anderson) between simultaneous core partitions for two relatively prime numbers $a$ and $b$ and Dyck paths in an $a\times b$ rectangle. There are many open problems relating to the $q,t$-enumeration of these objects. We discuss lattice path combinatorics that arise in the study of $(a,b)$-cores, and present a number of results concerning the conjectured $q$-statistic.