Enumeration of lozenge tilings of halved hexagons with a boundary defect

2015/10/15 by Rohatgi, Ranjan
#05A15 #05C70 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1510.04486

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.

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