Function rankFromRow

Computes the rank of a Row.

The numbering starts at 0 (rounds) and runs to n! - 1 (back rounds). Numbering is in "reverse colex order" (Knuth 7.2.1.2); i.e. if we reflect each row from right to left they would be in reverse lexicographic order.

  0: 123456
  1: 213456
  2: 132456
  3: 312456
...
717: 645321
718: 564321
719: 654321
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> rankFromRow([2, 1, 4, 3], Pricker.Stage.Minimus));
7
> rankFromRow([6, 5, 4, 3, 2, 1], Pricker.Stage.Minor));
719
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The rank is computed by counting the number of "inversions" to the left of each position (the left inversion count, l). The vector of counts is then interpreted as a single number using the Factorial number system.

            ┌───┬───┬───┬───┐
       row: │ 2 │ 1 │ 4 │ 3 │
            ├───┼───┼───┼───┤
inversions: │ - │ 1 │ 0 │ 1 │
            └───┴───┴───┴───┘

rank = (1 × 1) + (0 × 2) + (1 × 6) = 7
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This scheme has been chosen for compatibility with the data tables that are produced by Philip Saddleton's "StedTurn" software.