File:0426 1537 inversions matrix.svg

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Description
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).

Related images of Walsh permutation 421
part of Related sets of 3-bit Walsh permutations
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Watchduck
You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".

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current12:18, 18 June 2022Thumbnail for version as of 12:18, 18 June 2022670 × 758 (17 KB)Watchduck (talk | contribs)uploaded with Pywikibot

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