Template:Permutations of 8 elements; inversions matrix

Image set Permutations of 8 elements; inversions matrix

This is: left action last ⋅ first There is also: right action first ⋅ last This is the Rothe diagram of a permutation of 0...7. The black dots form the (left) permutation matrix, and the gray squares are elements of the inversion set. Each one is marked with the pair of places (gray) and values (black). The two vectors (brown) show the number of inversions in the respective row or column. The horizontal vector is the right inversion-count (r), and the vertical one is the inversion vector (v). In the bottom right square is the total number of inversions, the sum of both vectors. See Inversion (discrete mathematics).