Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000506
Mapping
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000506: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => [1,2] => [1,1]
 => [1]
 => 0
[1,-2] => [1,2] => [1,1]
 => [1]
 => 0
[-1,2] => [1,2] => [1,1]
 => [1]
 => 0
[-1,-2] => [1,2] => [1,1]
 => [1]
 => 0
[1,2,3] => [1,2,3] => [1,1,1]
 => [1,1]
 => 1
[1,2,-3] => [1,2,3] => [1,1,1]
 => [1,1]
 => 1
[1,-2,3] => [1,2,3] => [1,1,1]
 => [1,1]
 => 1
[1,-2,-3] => [1,2,3] => [1,1,1]
 => [1,1]
 => 1
[-1,2,3] => [1,2,3] => [1,1,1]
 => [1,1]
 => 1
[-1,2,-3] => [1,2,3] => [1,1,1]
 => [1,1]
 => 1
[-1,-2,3] => [1,2,3] => [1,1,1]
 => [1,1]
 => 1
[-1,-2,-3] => [1,2,3] => [1,1,1]
 => [1,1]
 => 1
[1,3,2] => [1,3,2] => [2,1]
 => [1]
 => 0
[1,3,-2] => [1,3,2] => [2,1]
 => [1]
 => 0
[1,-3,2] => [1,3,2] => [2,1]
 => [1]
 => 0
[1,-3,-2] => [1,3,2] => [2,1]
 => [1]
 => 0
[-1,3,2] => [1,3,2] => [2,1]
 => [1]
 => 0
[-1,3,-2] => [1,3,2] => [2,1]
 => [1]
 => 0
[-1,-3,2] => [1,3,2] => [2,1]
 => [1]
 => 0
[-1,-3,-2] => [1,3,2] => [2,1]
 => [1]
 => 0
[2,1,3] => [2,1,3] => [2,1]
 => [1]
 => 0
[2,1,-3] => [2,1,3] => [2,1]
 => [1]
 => 0
[2,-1,3] => [2,1,3] => [2,1]
 => [1]
 => 0
[2,-1,-3] => [2,1,3] => [2,1]
 => [1]
 => 0
[-2,1,3] => [2,1,3] => [2,1]
 => [1]
 => 0
[-2,1,-3] => [2,1,3] => [2,1]
 => [1]
 => 0
[-2,-1,3] => [2,1,3] => [2,1]
 => [1]
 => 0
[-2,-1,-3] => [2,1,3] => [2,1]
 => [1]
 => 0
[3,2,1] => [3,2,1] => [2,1]
 => [1]
 => 0
[3,2,-1] => [3,2,1] => [2,1]
 => [1]
 => 0
[3,-2,1] => [3,2,1] => [2,1]
 => [1]
 => 0
[3,-2,-1] => [3,2,1] => [2,1]
 => [1]
 => 0
[-3,2,1] => [3,2,1] => [2,1]
 => [1]
 => 0
[-3,2,-1] => [3,2,1] => [2,1]
 => [1]
 => 0
[-3,-2,1] => [3,2,1] => [2,1]
 => [1]
 => 0
[-3,-2,-1] => [3,2,1] => [2,1]
 => [1]
 => 0
[1,2,3,4] => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 0
[1,2,3,-4] => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 0
[1,2,-3,4] => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 0
[1,2,-3,-4] => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 0
[1,-2,3,4] => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 0
[1,-2,3,-4] => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 0
[1,-2,-3,4] => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 0
[1,-2,-3,-4] => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,2,3,4] => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,2,3,-4] => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,2,-3,4] => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,2,-3,-4] => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,-2,3,4] => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 0
[-1,-2,3,-4] => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 0
Description
The number of standard desarrangement tableaux of shape equal to the given partition. A '''standard desarrangement tableau''' is a standard tableau whose first ascent is even. Here, an ascent of a standard tableau is an entry $i$ such that $i+1$ appears to the right or above $i$ in the tableau (with respect to English tableau notation). This is also the nullity of the random-to-random operator (and the random-to-top) operator acting on the simple module of the symmetric group indexed by the given partition. See also: * [[St000046]]: The largest eigenvalue of the random to random operator acting on the simple module corresponding to the given partition * [[St000500]]: Eigenvalues of the random-to-random operator acting on the regular representation.
Matching statistic: St001857
(load all 5 compositions to match this statistic)
Mapping
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001857: Signed permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 50%
Values
[1,2] => [1,2] => [2,1] => [2,1] => 0
[1,-2] => [1,2] => [2,1] => [2,1] => 0
[-1,2] => [1,2] => [2,1] => [2,1] => 0
[-1,-2] => [1,2] => [2,1] => [2,1] => 0
[1,2,3] => [1,2,3] => [3,2,1] => [3,2,1] => 1
[1,2,-3] => [1,2,3] => [3,2,1] => [3,2,1] => 1
[1,-2,3] => [1,2,3] => [3,2,1] => [3,2,1] => 1
[1,-2,-3] => [1,2,3] => [3,2,1] => [3,2,1] => 1
[-1,2,3] => [1,2,3] => [3,2,1] => [3,2,1] => 1
[-1,2,-3] => [1,2,3] => [3,2,1] => [3,2,1] => 1
[-1,-2,3] => [1,2,3] => [3,2,1] => [3,2,1] => 1
[-1,-2,-3] => [1,2,3] => [3,2,1] => [3,2,1] => 1
[1,3,2] => [1,3,2] => [3,1,2] => [3,1,2] => 0
[1,3,-2] => [1,3,2] => [3,1,2] => [3,1,2] => 0
[1,-3,2] => [1,3,2] => [3,1,2] => [3,1,2] => 0
[1,-3,-2] => [1,3,2] => [3,1,2] => [3,1,2] => 0
[-1,3,2] => [1,3,2] => [3,1,2] => [3,1,2] => 0
[-1,3,-2] => [1,3,2] => [3,1,2] => [3,1,2] => 0
[-1,-3,2] => [1,3,2] => [3,1,2] => [3,1,2] => 0
[-1,-3,-2] => [1,3,2] => [3,1,2] => [3,1,2] => 0
[2,1,3] => [2,1,3] => [2,3,1] => [2,3,1] => 0
[2,1,-3] => [2,1,3] => [2,3,1] => [2,3,1] => 0
[2,-1,3] => [2,1,3] => [2,3,1] => [2,3,1] => 0
[2,-1,-3] => [2,1,3] => [2,3,1] => [2,3,1] => 0
[-2,1,3] => [2,1,3] => [2,3,1] => [2,3,1] => 0
[-2,1,-3] => [2,1,3] => [2,3,1] => [2,3,1] => 0
[-2,-1,3] => [2,1,3] => [2,3,1] => [2,3,1] => 0
[-2,-1,-3] => [2,1,3] => [2,3,1] => [2,3,1] => 0
[3,2,1] => [3,2,1] => [1,2,3] => [1,2,3] => 0
[3,2,-1] => [3,2,1] => [1,2,3] => [1,2,3] => 0
[3,-2,1] => [3,2,1] => [1,2,3] => [1,2,3] => 0
[3,-2,-1] => [3,2,1] => [1,2,3] => [1,2,3] => 0
[-3,2,1] => [3,2,1] => [1,2,3] => [1,2,3] => 0
[-3,2,-1] => [3,2,1] => [1,2,3] => [1,2,3] => 0
[-3,-2,1] => [3,2,1] => [1,2,3] => [1,2,3] => 0
[-3,-2,-1] => [3,2,1] => [1,2,3] => [1,2,3] => 0
[1,2,3,4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 0
[1,2,3,-4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 0
[1,2,-3,4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 0
[1,2,-3,-4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 0
[1,-2,3,4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 0
[1,-2,3,-4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 0
[1,-2,-3,4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 0
[1,-2,-3,-4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 0
[-1,2,3,4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 0
[-1,2,3,-4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 0
[-1,2,-3,4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 0
[-1,2,-3,-4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 0
[-1,-2,3,4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 0
[-1,-2,3,-4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 0
[-1,-2,-3,4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 0
[-1,-2,-3,-4] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ? = 0
[1,2,4,3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[1,2,4,-3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[1,2,-4,3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[1,2,-4,-3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[1,-2,4,3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[1,-2,4,-3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[1,-2,-4,3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[1,-2,-4,-3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[-1,2,4,3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[-1,2,4,-3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[-1,2,-4,3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[-1,2,-4,-3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[-1,-2,4,3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[-1,-2,4,-3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[-1,-2,-4,3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[-1,-2,-4,-3] => [1,2,4,3] => [4,3,1,2] => [4,3,1,2] => ? = 1
[1,3,2,4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[1,3,2,-4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[1,3,-2,4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[1,3,-2,-4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[1,-3,2,4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[1,-3,2,-4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[1,-3,-2,4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[1,-3,-2,-4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[-1,3,2,4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[-1,3,2,-4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[-1,3,-2,4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[-1,3,-2,-4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[-1,-3,2,4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[-1,-3,2,-4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[-1,-3,-2,4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[-1,-3,-2,-4] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => ? = 1
[1,3,4,2] => [1,3,4,2] => [4,2,1,3] => [4,2,1,3] => ? = 0
[1,3,4,-2] => [1,3,4,2] => [4,2,1,3] => [4,2,1,3] => ? = 0
Description
The number of edges in the reduced word graph of a signed permutation. The reduced word graph of a signed permutation $\pi$ has the reduced words of $\pi$ as vertices and an edge between two reduced words if they differ by exactly one braid move.