rectification; Abhyankar-Sathaye embedding problem; variable totally positive matrices; positive Grassmannian; minors; Plücker coordinates; matrix completion problem; arrangements of equal minors; weakly separated sets; sorted sets; triangulations; thrackles; cluster algebras; plabic graphs; Laurent phenomenon; alcoved polytopes; hypersimplices; affine Coxeter arrangement; Eulerian numbers; chain reactions of mutations; mutation distance; honeycombs; Gröbner bases; Schur positivity 