University of Minnesota Combinatorics Seminar
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Abstract |
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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. |