Lozenge tilings of hexagons with holes on three crossing lines

Problems in the Enumeration of Tilings

“…Byun generalized the shuffling phenomenon for a triad of bowties in [19]. He showed that the tiling number of a hexagon with holes on three crossing lines only changes by a simple multiplicative factor if we flip the central triangular hole and then translate these lines of holes (see Theorem 2.1 in [7]). See Figure 3.3 for an illustration.…”

“…Problem 16. (a) Generalizing Byun's Theorem 2.1(b) in [7] to generating functions of cyclically symmetric tilings using the weight wt 1 (or some specialization).…”