W-associahedra have the non-leaving-face property. (May 2017) - Williams, Nathan
Abstract: We use a projection argument to uniformly prove that W -permutahedra and W -associahedra have the property that if v, v ′ are two vertices on the same face f, then any geodesic between v and v ′ does not leave f . In type A, we show that our geometric projection recovers a slight modification of the combinatorial projection in Sleator et al. (1988).