- FindStat

Identifier

Mp00254: Permutations —Inverse fireworks map⟶ Permutations
St000058: Permutations ⟶ ℤ

Values

[1] => [1] => 1

[1,2] => [1,2] => 1

[2,1] => [2,1] => 2

[1,2,3] => [1,2,3] => 1

[1,3,2] => [1,3,2] => 2

[2,1,3] => [2,1,3] => 2

[2,3,1] => [1,3,2] => 2

[3,1,2] => [3,1,2] => 3

[3,2,1] => [3,2,1] => 2

[1,2,3,4] => [1,2,3,4] => 1

[1,2,4,3] => [1,2,4,3] => 2

[1,3,2,4] => [1,3,2,4] => 2

[1,3,4,2] => [1,2,4,3] => 2

[1,4,2,3] => [1,4,2,3] => 3

[1,4,3,2] => [1,4,3,2] => 2

[2,1,3,4] => [2,1,3,4] => 2

[2,1,4,3] => [2,1,4,3] => 2

[2,3,1,4] => [1,3,2,4] => 2

[2,3,4,1] => [1,2,4,3] => 2

[2,4,1,3] => [2,4,1,3] => 4

[2,4,3,1] => [1,4,3,2] => 2

[3,1,2,4] => [3,1,2,4] => 3

[3,1,4,2] => [2,1,4,3] => 2

[3,2,1,4] => [3,2,1,4] => 2

[3,2,4,1] => [2,1,4,3] => 2

[3,4,1,2] => [2,4,1,3] => 4

[3,4,2,1] => [1,4,3,2] => 2

[4,1,2,3] => [4,1,2,3] => 4

[4,1,3,2] => [4,1,3,2] => 3

[4,2,1,3] => [4,2,1,3] => 3

[4,2,3,1] => [4,1,3,2] => 3

[4,3,1,2] => [4,3,1,2] => 4

[4,3,2,1] => [4,3,2,1] => 2

[1,2,3,4,5] => [1,2,3,4,5] => 1

[1,2,3,5,4] => [1,2,3,5,4] => 2

[1,2,4,3,5] => [1,2,4,3,5] => 2

[1,2,4,5,3] => [1,2,3,5,4] => 2

[1,2,5,3,4] => [1,2,5,3,4] => 3

[1,2,5,4,3] => [1,2,5,4,3] => 2

[1,3,2,4,5] => [1,3,2,4,5] => 2

[1,3,2,5,4] => [1,3,2,5,4] => 2

[1,3,4,2,5] => [1,2,4,3,5] => 2

[1,3,4,5,2] => [1,2,3,5,4] => 2

[1,3,5,2,4] => [1,3,5,2,4] => 4

[1,3,5,4,2] => [1,2,5,4,3] => 2

[1,4,2,3,5] => [1,4,2,3,5] => 3

[1,4,2,5,3] => [1,3,2,5,4] => 2

[1,4,3,2,5] => [1,4,3,2,5] => 2

[1,4,3,5,2] => [1,3,2,5,4] => 2

[1,4,5,2,3] => [1,3,5,2,4] => 4

[1,4,5,3,2] => [1,2,5,4,3] => 2

[1,5,2,3,4] => [1,5,2,3,4] => 4

[1,5,2,4,3] => [1,5,2,4,3] => 3

[1,5,3,2,4] => [1,5,3,2,4] => 3

[1,5,3,4,2] => [1,5,2,4,3] => 3

[1,5,4,2,3] => [1,5,4,2,3] => 4

[1,5,4,3,2] => [1,5,4,3,2] => 2

[2,1,3,4,5] => [2,1,3,4,5] => 2

[2,1,3,5,4] => [2,1,3,5,4] => 2

[2,1,4,3,5] => [2,1,4,3,5] => 2

[2,1,4,5,3] => [2,1,3,5,4] => 2

[2,1,5,3,4] => [2,1,5,3,4] => 6

[2,1,5,4,3] => [2,1,5,4,3] => 2

[2,3,1,4,5] => [1,3,2,4,5] => 2

[2,3,1,5,4] => [1,3,2,5,4] => 2

[2,3,4,1,5] => [1,2,4,3,5] => 2

[2,3,4,5,1] => [1,2,3,5,4] => 2

[2,3,5,1,4] => [1,3,5,2,4] => 4

[2,3,5,4,1] => [1,2,5,4,3] => 2

[2,4,1,3,5] => [2,4,1,3,5] => 4

[2,4,1,5,3] => [1,3,2,5,4] => 2

[2,4,3,1,5] => [1,4,3,2,5] => 2

[2,4,3,5,1] => [1,3,2,5,4] => 2

[2,4,5,1,3] => [1,3,5,2,4] => 4

[2,4,5,3,1] => [1,2,5,4,3] => 2

[2,5,1,3,4] => [2,5,1,3,4] => 5

[2,5,1,4,3] => [2,5,1,4,3] => 4

[2,5,3,1,4] => [1,5,3,2,4] => 3

[2,5,3,4,1] => [1,5,2,4,3] => 3

[2,5,4,1,3] => [2,5,4,1,3] => 5

[2,5,4,3,1] => [1,5,4,3,2] => 2

[3,1,2,4,5] => [3,1,2,4,5] => 3

[3,1,2,5,4] => [3,1,2,5,4] => 6

[3,1,4,2,5] => [2,1,4,3,5] => 2

[3,1,4,5,2] => [2,1,3,5,4] => 2

[3,1,5,2,4] => [3,1,5,2,4] => 5

[3,1,5,4,2] => [2,1,5,4,3] => 2

[3,2,1,4,5] => [3,2,1,4,5] => 2

[3,2,1,5,4] => [3,2,1,5,4] => 2

[3,2,4,1,5] => [2,1,4,3,5] => 2

[3,2,4,5,1] => [2,1,3,5,4] => 2

[3,2,5,1,4] => [3,2,5,1,4] => 4

[3,2,5,4,1] => [2,1,5,4,3] => 2

[3,4,1,2,5] => [2,4,1,3,5] => 4

[3,4,1,5,2] => [1,3,2,5,4] => 2

[3,4,2,1,5] => [1,4,3,2,5] => 2

[3,4,2,5,1] => [1,3,2,5,4] => 2

[3,4,5,1,2] => [1,3,5,2,4] => 4

[3,4,5,2,1] => [1,2,5,4,3] => 2

[3,5,1,2,4] => [3,5,1,2,4] => 6

[3,5,1,4,2] => [2,5,1,4,3] => 4

>>> Load all 2656 entries. <<<

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Description

The order of a permutation.
$\operatorname{ord}(\pi)$ is given by the minimial $k$ for which $\pi^k$ is the identity permutation.

Map

Inverse fireworks map

Description

Sends a permutation to an inverse fireworks permutation.
A permutation $\sigma$ is inverse fireworks if its inverse avoids the vincular pattern $3-12$. The inverse fireworks map sends any permutation $\sigma$ to an inverse fireworks permutation that is below $\sigma$ in left weak order and has the same Rajchgot index St001759The Rajchgot index of a permutation..