Enumeration of Lozenge Tilings of Halved Hexagons with a Boundary Defect

Ranjan Rohatgi

Abstract


We generalize a special case of a theorem of Proctor on the enumeration of lozenge tilings of a hexagon with a maximal staircase removed using Kuo’s graphical condensation method. Additionally, we prove a formula for a weighted version of the given region. The result also extends work of Ciucu and Fischer. By applying the factorization theorem of Ciucu, we are also able to generalize a special case of MacMahon’s boxed plane partition formula. 


Keywords


tilings; perfect matchings

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