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Rosengren found an explicit formula for a certain weighted enumeration oflozenge tilings of a hexagon with an arbitrary triangular hole. He pointed outthat a certain ratio corresponding to two such regions has a nice productformula. In this paper, we generalize this to hexagons with arbitrary collinearholes. It turns out that, by using same approach, we can also generalizeCiucu's work on the number and the number of centrally symmetric tilings of ahexagon with a fern removed from its center. This proves a recent conjecture ofCiucu.

Three product formulas for ratios of tiling counts of hexagons with collinear holes