Lozenge tilings of hexagons with holes on three crossing lines

2020/08/03 by Byun, Seok Hyun
#05A15 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2008.00591

Abstract

The enumeration of lozenge tilings of hexagons with holes has received much attention during the last three decades. One notable feature is that a lot of the recent development involved Kuo's graphical condensation. Motivated by Ciucu, Lai and Rohatgi's work on tilings of hexagons with a removed triad of bowties, in this paper, we show that the ratio of numbers of lozenge tilings of two more general regions is expressed as a simple product formula. Our proof does not involve the graphical condensation method. The proof is short and direct. We also provide a corresponding formula for cyclically symmetric lozenge tilings. Several previous results can be easily deduced from our generalization.

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