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Three product formulas for ratios of tiling counts of hexagons with collinear holes
Seok Hyun Byun
Rosengren found an explicit formula for a certain weighted enumeration of lozenge tilings of a hexagon with an arbitrary triangular hole. He pointed out that a certain ratio corres…
math.CO2019
A short proof of two shuffling theorems for tilings and a weighted generalization
Seok Hyun Byun
Recently, Lai and Rohatgi discovered a shuffling theorem for lozenge tilings of doubly-dented hexagons, which generalized the earlier work of Ciucu. Later, Lai proved an analogous…