Let votin\quotmaxv otin\quotmaxvotin\quotmax and w≥vw\geq vw≥v, let b1aσ=v−1wb1a\sigma=v^{-1}wb1aσ=v−1w be the resulting permutation decorated by declaring a fixed index jjj black if j∈v−1[k]j\in v^{-1}[k]j∈v−1[k], and set I=v−1[k]I=v^{-1}[k]I=v−1[k].…