- FindStat

Identifier

Mp00163: Signed permutations —permutation⟶ Permutations
Mp00252: Permutations —restriction⟶ Permutations
Mp00131: Permutations —descent bottoms⟶ Binary words
St001491: Binary words ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,3,2,4] => [1,3,2,4] => [1,3,2] => 01 => 1

[1,3,2,-4] => [1,3,2,4] => [1,3,2] => 01 => 1

[1,3,-2,4] => [1,3,2,4] => [1,3,2] => 01 => 1

[1,3,-2,-4] => [1,3,2,4] => [1,3,2] => 01 => 1

[1,-3,2,4] => [1,3,2,4] => [1,3,2] => 01 => 1

[1,-3,2,-4] => [1,3,2,4] => [1,3,2] => 01 => 1

[1,-3,-2,4] => [1,3,2,4] => [1,3,2] => 01 => 1

[1,-3,-2,-4] => [1,3,2,4] => [1,3,2] => 01 => 1

[-1,3,2,4] => [1,3,2,4] => [1,3,2] => 01 => 1

[-1,3,2,-4] => [1,3,2,4] => [1,3,2] => 01 => 1

[-1,3,-2,4] => [1,3,2,4] => [1,3,2] => 01 => 1

[-1,3,-2,-4] => [1,3,2,4] => [1,3,2] => 01 => 1

[-1,-3,2,4] => [1,3,2,4] => [1,3,2] => 01 => 1

[-1,-3,2,-4] => [1,3,2,4] => [1,3,2] => 01 => 1

[-1,-3,-2,4] => [1,3,2,4] => [1,3,2] => 01 => 1

[-1,-3,-2,-4] => [1,3,2,4] => [1,3,2] => 01 => 1

[1,3,4,2] => [1,3,4,2] => [1,3,2] => 01 => 1

[1,3,4,-2] => [1,3,4,2] => [1,3,2] => 01 => 1

[1,3,-4,2] => [1,3,4,2] => [1,3,2] => 01 => 1

[1,3,-4,-2] => [1,3,4,2] => [1,3,2] => 01 => 1

[1,-3,4,2] => [1,3,4,2] => [1,3,2] => 01 => 1

[1,-3,4,-2] => [1,3,4,2] => [1,3,2] => 01 => 1

[1,-3,-4,2] => [1,3,4,2] => [1,3,2] => 01 => 1

[1,-3,-4,-2] => [1,3,4,2] => [1,3,2] => 01 => 1

[-1,3,4,2] => [1,3,4,2] => [1,3,2] => 01 => 1

[-1,3,4,-2] => [1,3,4,2] => [1,3,2] => 01 => 1

[-1,3,-4,2] => [1,3,4,2] => [1,3,2] => 01 => 1

[-1,3,-4,-2] => [1,3,4,2] => [1,3,2] => 01 => 1

[-1,-3,4,2] => [1,3,4,2] => [1,3,2] => 01 => 1

[-1,-3,4,-2] => [1,3,4,2] => [1,3,2] => 01 => 1

[-1,-3,-4,2] => [1,3,4,2] => [1,3,2] => 01 => 1

[-1,-3,-4,-2] => [1,3,4,2] => [1,3,2] => 01 => 1

[1,4,3,2] => [1,4,3,2] => [1,3,2] => 01 => 1

[1,4,3,-2] => [1,4,3,2] => [1,3,2] => 01 => 1

[1,4,-3,2] => [1,4,3,2] => [1,3,2] => 01 => 1

[1,4,-3,-2] => [1,4,3,2] => [1,3,2] => 01 => 1

[1,-4,3,2] => [1,4,3,2] => [1,3,2] => 01 => 1

[1,-4,3,-2] => [1,4,3,2] => [1,3,2] => 01 => 1

[1,-4,-3,2] => [1,4,3,2] => [1,3,2] => 01 => 1

[1,-4,-3,-2] => [1,4,3,2] => [1,3,2] => 01 => 1

[-1,4,3,2] => [1,4,3,2] => [1,3,2] => 01 => 1

[-1,4,3,-2] => [1,4,3,2] => [1,3,2] => 01 => 1

[-1,4,-3,2] => [1,4,3,2] => [1,3,2] => 01 => 1

[-1,4,-3,-2] => [1,4,3,2] => [1,3,2] => 01 => 1

[-1,-4,3,2] => [1,4,3,2] => [1,3,2] => 01 => 1

[-1,-4,3,-2] => [1,4,3,2] => [1,3,2] => 01 => 1

[-1,-4,-3,2] => [1,4,3,2] => [1,3,2] => 01 => 1

[-1,-4,-3,-2] => [1,4,3,2] => [1,3,2] => 01 => 1

[2,1,3,4] => [2,1,3,4] => [2,1,3] => 10 => 1

[2,1,3,-4] => [2,1,3,4] => [2,1,3] => 10 => 1

[2,1,-3,4] => [2,1,3,4] => [2,1,3] => 10 => 1

[2,1,-3,-4] => [2,1,3,4] => [2,1,3] => 10 => 1

[2,-1,3,4] => [2,1,3,4] => [2,1,3] => 10 => 1

[2,-1,3,-4] => [2,1,3,4] => [2,1,3] => 10 => 1

[2,-1,-3,4] => [2,1,3,4] => [2,1,3] => 10 => 1

[2,-1,-3,-4] => [2,1,3,4] => [2,1,3] => 10 => 1

[-2,1,3,4] => [2,1,3,4] => [2,1,3] => 10 => 1

[-2,1,3,-4] => [2,1,3,4] => [2,1,3] => 10 => 1

[-2,1,-3,4] => [2,1,3,4] => [2,1,3] => 10 => 1

[-2,1,-3,-4] => [2,1,3,4] => [2,1,3] => 10 => 1

[-2,-1,3,4] => [2,1,3,4] => [2,1,3] => 10 => 1

[-2,-1,3,-4] => [2,1,3,4] => [2,1,3] => 10 => 1

[-2,-1,-3,4] => [2,1,3,4] => [2,1,3] => 10 => 1

[-2,-1,-3,-4] => [2,1,3,4] => [2,1,3] => 10 => 1

[2,1,4,3] => [2,1,4,3] => [2,1,3] => 10 => 1

[2,1,4,-3] => [2,1,4,3] => [2,1,3] => 10 => 1

[2,1,-4,3] => [2,1,4,3] => [2,1,3] => 10 => 1

[2,1,-4,-3] => [2,1,4,3] => [2,1,3] => 10 => 1

[2,-1,4,3] => [2,1,4,3] => [2,1,3] => 10 => 1

[2,-1,4,-3] => [2,1,4,3] => [2,1,3] => 10 => 1

[2,-1,-4,3] => [2,1,4,3] => [2,1,3] => 10 => 1

[2,-1,-4,-3] => [2,1,4,3] => [2,1,3] => 10 => 1

[-2,1,4,3] => [2,1,4,3] => [2,1,3] => 10 => 1

[-2,1,4,-3] => [2,1,4,3] => [2,1,3] => 10 => 1

[-2,1,-4,3] => [2,1,4,3] => [2,1,3] => 10 => 1

[-2,1,-4,-3] => [2,1,4,3] => [2,1,3] => 10 => 1

[-2,-1,4,3] => [2,1,4,3] => [2,1,3] => 10 => 1

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search for individual values

searching the database for the individual values of this statistic

Description

The number of indecomposable projective-injective modules in the algebra corresponding to a subset.
Let $A_n=K[x]/(x^n)$.
We associate to a nonempty subset S of an (n-1)-set the module $M_S$, which is the direct sum of $A_n$-modules with indecomposable non-projective direct summands of dimension $i$ when $i$ is in $S$ (note that such modules have vector space dimension at most n-1). Then the corresponding algebra associated to S is the stable endomorphism ring of $M_S$. We decode the subset as a binary word so that for example the subset $S=\{1,3 \} $ of $\{1,2,3 \}$ is decoded as 101.

Map

descent bottoms

Description

The descent bottoms of a permutation as a binary word.

Map

permutation

Description

The permutation obtained by forgetting the colours.

Map

restriction

Description

The permutation obtained by removing the largest letter.
This map is undefined for the empty permutation.