Speaker: Tri Lai, University of Nebraska
Title: $q$-enumeration of lozenge tilings
Abstract: MacMahon's classical theorem on box plane partitions yields a $q$-enumeration of lozenge tilings of a hexagon on the triangular lattice. Even though the tiling numbers of many regions have been found, there are only a few known $q$-enumerations in the field of enumeration of tilings. In this talk we investigate several new $q$-enumerations of lozenge tilings. Our results also generalize MacMahon's theorem.