Arrays of permutations

Inversion (discrete mathematics) Template:Rdrup
Triangle of possible inversions of 8-element permutations	Permutation $373$ 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.

Template:Oeis	$6936$ $=(124875)(36)$	Template:Oeis	$20533$ $=(157842)(36)$
Template:Oeis     Chains of transpositions	$23616$ $=(15)(26)(37)(48)$	Template:Oeis     Rows of transpositions	$5167$ $=(12)(34)(56)(78)$
Template:Oeis     Transpositions     This array corrsponds to the inverted array of 2-element subsets: In place $(i,j)$ is the cycle $(j,j+i)$, e.g. $(18)$ in place $(7,1)$.	$36153=(18)$ In place $(i,j)$ is the set $\{i,i+j\}$.	Template:Oeis     Nested transpositions	$40319$ $=(18)(27)(36)(45)$
Template:Oeis     Circular shifts to the left in an interval	Error creating thumbnail: $5913$ $=(18765432)$	Error creating thumbnail: Template:Oeis     Circular shifts to the right in an interval	File:Example permutation matrix; circular shift, right.svg $35280$ $=(12345678)$
Circular shifts to the left, i.e. permutations whose cycle notation is of the form $(1n...32)$: Template:Oeis = 0, 1, 3, 9, 33, 153, 873, 5913...		Circular shifts to the right, i.e. permutations whose cycle notation is of the form $(123...n)$: Template:Oeis = 0, 1, 4, 18, 96, 600, 4320, 35280...