Matchings and Clusters on Plabic Fences

João Pedro Carvalho, Yucong Lei

Fix two positive braid words ${\beta }_{+},{\beta }_{-}$, and let $\text{Conf}({\beta }_{+},{\beta }_{-})$ be the corresponding (type A) double Bott-Samelson variety. Let $\beta$ be a double braid word containing $β_+,β_…