Arrays of permutations

Inversion (discrete mathematics)
Triangle of possible inversions of 8-element permutations	Permutation ${\mathit {373}}$ 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.

A211365	${\mathit {6936}}$ $=(124875)(36)$	A211366	${\mathit {20533}}$ $=(157842)(36)$
A211367     Chains of transpositions	${\mathit {23616}}$ $=(15)(26)(37)(48)$	A211368     Rows of transpositions	${\mathit {5167}}$ $=(12)(34)(56)(78)$
A211369     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 $(7,1)$.	${\mathit {36153}}=(18)$ In place $(i,j)$ is the set $\{i,i+j\}$.	A100630     Nested transpositions	${\mathit {40319}}$ $=(18)(27)(36)(45)$
A211370     Circular shifts to the left in an interval	${\mathit {5913}}$ $=(18765432)$	A051683     Circular shifts to the right in an interval	${\mathit {35280}}$ $=(12345678)$
Circular shifts to the left, i.e. permutations whose cycle notation is of the form $(1~n~...~3~2)$:  A007489 = 0, 1, 3, 9, 33, 153, 873, 5913...		Circular shifts to the right, i.e. permutations whose cycle notation is of the form $(1~2~3~...~n)$:  A001563 = 0, 1, 4, 18, 96, 600, 4320, 35280...