Identifier
Values
[1,2] => [1,2] => [1,2] => 0
[2,1] => [2,1] => [2,1] => 1
[1,2,3] => [1,2,3] => [1,2,3] => 0
[1,3,2] => [1,3,2] => [3,1,2] => 2
[2,1,3] => [2,1,3] => [2,1,3] => 1
[2,3,1] => [1,3,2] => [3,1,2] => 2
[3,1,2] => [3,1,2] => [1,3,2] => 1
[3,2,1] => [3,2,1] => [3,2,1] => 2
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,2,4,3] => [1,2,4,3] => [4,1,2,3] => 3
[1,3,2,4] => [1,3,2,4] => [3,1,2,4] => 2
[1,3,4,2] => [1,2,4,3] => [4,1,2,3] => 3
[1,4,2,3] => [1,4,2,3] => [1,4,2,3] => 2
[1,4,3,2] => [1,4,3,2] => [4,3,1,2] => 3
[2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 1
[2,1,4,3] => [2,1,4,3] => [2,4,1,3] => 2
[2,3,1,4] => [1,3,2,4] => [3,1,2,4] => 2
[2,3,4,1] => [1,2,4,3] => [4,1,2,3] => 3
[2,4,1,3] => [2,4,1,3] => [4,2,1,3] => 3
[2,4,3,1] => [1,4,3,2] => [4,3,1,2] => 3
[3,1,2,4] => [3,1,2,4] => [1,3,2,4] => 1
[3,1,4,2] => [2,1,4,3] => [2,4,1,3] => 2
[3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 2
[3,2,4,1] => [2,1,4,3] => [2,4,1,3] => 2
[3,4,1,2] => [2,4,1,3] => [4,2,1,3] => 3
[3,4,2,1] => [1,4,3,2] => [4,3,1,2] => 3
[4,1,2,3] => [4,1,2,3] => [1,2,4,3] => 1
[4,1,3,2] => [4,1,3,2] => [4,1,3,2] => 3
[4,2,1,3] => [4,2,1,3] => [2,1,4,3] => 1
[4,2,3,1] => [4,1,3,2] => [4,1,3,2] => 3
[4,3,1,2] => [4,3,1,2] => [1,4,3,2] => 2
[4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 3
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Description
The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$.
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..
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00067Foata bijection.