Product formula conjecture for centrally symmetric tilings of $R^{\odot}$-type regions

Let $R^{\odot}_{x,yz}(\textbf{a};\ \textbf{c};\ \textbf{b})$ be the region described in the paper, and consider its tilings invariant under $180^{\circ}$ rotations. Product formula conjecture. The number of centrally symmetric tilings of the region $R^{\odot}_{x,yz}(\textbf{a};\ \textbf{c};\ \textbf{b})$ is always given by a simple product formula. The conjecture concerns explicit enumeration of centrally symmetric lozenge tilings of these regions; it was recently proved by Rosengren using lattice path combinatorics and a Selberg integral.