Processing math: 100%

Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000770
Mapping
Mp00170: Permutations —to signed permutation⟶ Signed permutations
Mp00281: Signed permutations —rowmotion⟶ Signed permutations
Mp00166: Signed permutations —even cycle type⟶ Integer partitions
St000770: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[2,3,1] => [2,3,1] => [2,1,-3] => [2]
 => 2
[3,2,1] => [3,2,1] => [1,2,-3] => [1,1]
 => 1
[1,3,4,2] => [1,3,4,2] => [-4,2,3,1] => [1,1]
 => 1
[1,4,3,2] => [1,4,3,2] => [-4,3,2,1] => [2]
 => 2
[2,1,4,3] => [2,1,4,3] => [1,-4,3,2] => [1,1]
 => 1
[2,3,1,4] => [2,3,1,4] => [2,1,-4,3] => [2]
 => 2
[2,3,4,1] => [2,3,4,1] => [3,1,2,-4] => [3]
 => 3
[2,4,3,1] => [2,4,3,1] => [3,2,1,-4] => [2,1]
 => 4
[3,2,1,4] => [3,2,1,4] => [1,2,-4,3] => [1,1]
 => 1
[3,2,4,1] => [3,2,4,1] => [1,3,2,-4] => [2,1]
 => 4
[3,4,2,1] => [3,4,2,1] => [2,1,3,-4] => [2,1]
 => 4
[4,1,2,3] => [4,1,2,3] => [3,-4,1,2] => [2]
 => 2
[4,2,3,1] => [4,2,3,1] => [2,3,1,-4] => [3]
 => 3
[4,3,2,1] => [4,3,2,1] => [1,2,3,-4] => [1,1,1]
 => 1
[1,2,4,5,3] => [1,2,4,5,3] => [-5,1,3,4,2] => [1,1]
 => 1
[1,2,5,4,3] => [1,2,5,4,3] => [-5,1,4,3,2] => [2]
 => 2
[1,3,2,5,4] => [1,3,2,5,4] => [-5,2,1,4,3] => [1,1]
 => 1
[1,3,4,2,5] => [1,3,4,2,5] => [-5,2,3,1,4] => [1,1]
 => 1
[1,3,4,5,2] => [1,3,4,5,2] => [-5,2,3,4,1] => [1,1,1]
 => 1
[1,3,5,4,2] => [1,3,5,4,2] => [-5,2,4,3,1] => [2,1]
 => 4
[1,4,3,2,5] => [1,4,3,2,5] => [-5,3,2,1,4] => [2]
 => 2
[1,4,3,5,2] => [1,4,3,5,2] => [-5,3,2,4,1] => [2,1]
 => 4
[1,4,5,3,2] => [1,4,5,3,2] => [-5,3,4,2,1] => [3]
 => 3
[1,5,2,3,4] => [1,5,2,3,4] => [-5,4,1,2,3] => [2]
 => 2
[1,5,3,4,2] => [1,5,3,4,2] => [-5,4,2,3,1] => [3]
 => 3
[1,5,4,3,2] => [1,5,4,3,2] => [-5,4,3,2,1] => [2,1]
 => 4
[2,1,3,5,4] => [2,1,3,5,4] => [1,-5,2,4,3] => [1,1]
 => 1
[2,1,4,3,5] => [2,1,4,3,5] => [1,-5,3,2,4] => [1,1]
 => 1
[2,1,4,5,3] => [2,1,4,5,3] => [1,-5,3,4,2] => [1,1,1]
 => 1
[2,1,5,4,3] => [2,1,5,4,3] => [1,-5,4,3,2] => [2,1]
 => 4
[2,3,1,4,5] => [2,3,1,4,5] => [2,1,-5,3,4] => [2]
 => 2
[2,3,1,5,4] => [2,3,1,5,4] => [2,1,-5,4,3] => [2,1]
 => 4
[2,3,4,1,5] => [2,3,4,1,5] => [3,1,2,-5,4] => [3]
 => 3
[2,3,4,5,1] => [2,3,4,5,1] => [4,1,2,3,-5] => [4]
 => 4
[2,3,5,4,1] => [2,3,5,4,1] => [4,1,3,2,-5] => [3,1]
 => 5
[2,4,3,1,5] => [2,4,3,1,5] => [3,2,1,-5,4] => [2,1]
 => 4
[2,4,3,5,1] => [2,4,3,5,1] => [4,2,1,3,-5] => [3,1]
 => 5
[2,4,5,3,1] => [2,4,5,3,1] => [4,2,3,1,-5] => [2,1,1]
 => 5
[2,5,1,3,4] => [2,5,1,3,4] => [4,1,-5,2,3] => [3]
 => 3
[2,5,3,4,1] => [2,5,3,4,1] => [4,3,1,2,-5] => [4]
 => 4
[2,5,4,3,1] => [2,5,4,3,1] => [4,3,2,1,-5] => [2,2]
 => 2
[3,1,4,5,2] => [3,1,4,5,2] => [2,-5,3,4,1] => [1,1]
 => 1
[3,1,5,4,2] => [3,1,5,4,2] => [2,-5,4,3,1] => [2]
 => 2
[3,2,1,4,5] => [3,2,1,4,5] => [1,2,-5,3,4] => [1,1]
 => 1
[3,2,1,5,4] => [3,2,1,5,4] => [1,2,-5,4,3] => [1,1,1]
 => 1
[3,2,4,1,5] => [3,2,4,1,5] => [1,3,2,-5,4] => [2,1]
 => 4
[3,2,4,5,1] => [3,2,4,5,1] => [1,4,2,3,-5] => [3,1]
 => 5
[3,2,5,4,1] => [3,2,5,4,1] => [1,4,3,2,-5] => [2,1,1]
 => 5
[3,4,1,5,2] => [3,4,1,5,2] => [3,2,-5,4,1] => [1,1]
 => 1
[3,4,2,1,5] => [3,4,2,1,5] => [2,1,3,-5,4] => [2,1]
 => 4
Description
The major index of an integer partition when read from bottom to top. This is the sum of the positions of the corners of the shape of an integer partition when reading from bottom to top. For example, the partition λ=(8,6,6,4,3,3) has corners at positions 3,6,9, and 13, giving a major index of 31.