Processing math: 100%

Your data matches 1 statistic following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000936
(load all 2 compositions to match this statistic)
Mapping
St000936: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[2]
 => 0
[1,1]
 => 0
[3]
 => 0
[2,1]
 => 2
[1,1,1]
 => 0
[4]
 => 0
[3,1]
 => 1
[2,2]
 => 4
[2,1,1]
 => 1
[1,1,1,1]
 => 0
[5]
 => 0
[4,1]
 => 4
[3,2]
 => 1
[3,1,1]
 => 6
[2,2,1]
 => 1
[2,1,1,1]
 => 4
[1,1,1,1,1]
 => 0
[6]
 => 0
[5,1]
 => 3
[4,2]
 => 4
[4,1,1]
 => 7
[3,3]
 => 3
[3,2,1]
 => 10
[3,1,1,1]
 => 7
[2,2,2]
 => 3
[2,2,1,1]
 => 4
[2,1,1,1,1]
 => 3
[1,1,1,1,1,1]
 => 0
[7]
 => 0
[6,1]
 => 8
[5,2]
 => 11
[5,1,1]
 => 4
[4,3]
 => 9
[4,2,1]
 => 3
[4,1,1,1]
 => 14
[3,3,1]
 => 3
[3,2,2]
 => 3
[3,2,1,1]
 => 3
[3,1,1,1,1]
 => 4
[2,2,2,1]
 => 9
[2,2,1,1,1]
 => 11
[2,1,1,1,1,1]
 => 8
[1,1,1,1,1,1,1]
 => 0
[8]
 => 0
[7,1]
 => 7
[6,2]
 => 13
[6,1,1]
 => 9
[5,3]
 => 13
[5,2,1]
 => 18
[5,1,1,1]
 => 8
Description
The number of even values of the symmetric group character corresponding to the partition. For example, the character values of the irreducible representation S(2,2) are 2 on the conjugacy classes (4) and (2,2), 0 on the conjugacy classes (3,1) and (1,1,1,1), and −1 on the conjugace class (2,1,1). Therefore, the statistic on the partition (2,2) is 4. It is shown in [1] that the sum of the values of the statistic over all partitions of a given size is even.