Arrays of permutations

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Inversion (discrete mathematics) Rdrup.svg
Triangle of possible inversions of 8-element permutations
Permutation from the array below

These are some examples of similar permutations ordered in arrays.

Each permutation is represented by its:

  • place-based inversion set
  • Rothe diagram (including the matrix representation as dots)
  • left-inversion vector (0s represented by dots, the leading 0s omitted)
  • reverse colexicographic index, i.e. the left-inversion vector interpreted as a little-endian factorial number

For the last permutation in each array the corresponding permutation matrix is also shown.

Sloane'sA211367     Chains of transpositions

Sloane'sA211368     Rows of transpositions

Sloane'sA211369     Transpositions     This array corrsponds to the inverted array of 2-element subsets: In place is the cycle , e.g. in place .

In place is the set .
Sloane'sA100630     Nested transpositions

Sloane'sA211370     Circular shifts to the left in an interval

Sloane'sA051683     Circular shifts to the right in an interval

Circular shifts to the left,
i.e. permutations whose cycle notation is of the form :
Sloane'sA007489 = 0, 1, 3, 9, 33, 153, 873, 5913...

Circular shifts to the right,
i.e. permutations whose cycle notation is of the form :
Sloane'sA001563 = 0, 1, 4, 18, 96, 600, 4320, 35280...