University of Minnesota Combinatorics Seminar
Monday, December 9, 2013
11:15am in 213 Vincent Hall



A dual of MacMahon's theorem on plane partitions

Christian Krattenthaler

Universität Wien


Abstract

A classical theorem of MacMahon states that the number of rhombus tilings of any centrally symmetric hexagon drawn on the triangular lattice is given by a beautifully simple product formula. I shall present a kind of "dual" of this formula, which is in fact a limit relation between the "numbers" of rhombus tilings of infinite regions. The "actual" main theorem behind is a closed product formula for the number of rhombus tilings of a hexagon with a hole in its interior which has the form of four adjacent triangles. This is joint work with Mihai Ciucu.