Alpert–Kahle–MacPherson homological stability conjecture for sliding fifteen-puzzle configurations
Alpert–Kahle–MacPherson's conjecture. The inclusion of SFn(Rw,h)SF_n(R_{w,h})SFn(Rw,h) into Fn(R2)F_n(\mathbb{R}^2)Fn(R2) induces an isomorphism