Identifier
Identifier
Values
[] generating graphics... => 1
[1] generating graphics... => 1
[2] generating graphics... => 2
[1,1] generating graphics... => 0
[3] generating graphics... => 3
[2,1] generating graphics... => 1
[1,1,1] generating graphics... => 1
[4] generating graphics... => 5
[3,1] generating graphics... => 2
[2,2] generating graphics... => 3
[2,1,1] generating graphics... => 2
[1,1,1,1] generating graphics... => 1
[5] generating graphics... => 7
[4,1] generating graphics... => 5
[3,2] generating graphics... => 6
[3,1,1] generating graphics... => 5
[2,2,1] generating graphics... => 4
[2,1,1,1] generating graphics... => 3
[1,1,1,1,1] generating graphics... => 1
[6] generating graphics... => 11
[5,1] generating graphics... => 8
[4,2] generating graphics... => 15
[4,1,1] generating graphics... => 10
[3,3] generating graphics... => 4
[3,2,1] generating graphics... => 13
[3,1,1,1] generating graphics... => 10
[2,2,2] generating graphics... => 8
[2,2,1,1] generating graphics... => 5
[2,1,1,1,1] generating graphics... => 4
[1,1,1,1,1,1] generating graphics... => 1
[7] generating graphics... => 15
[6,1] generating graphics... => 15
[5,2] generating graphics... => 26
[5,1,1] generating graphics... => 19
[4,3] generating graphics... => 18
[4,2,1] generating graphics... => 36
[4,1,1,1] generating graphics... => 21
[3,3,1] generating graphics... => 18
[3,2,2] generating graphics... => 22
[3,2,1,1] generating graphics... => 28
[3,1,1,1,1] generating graphics... => 13
[2,2,2,1] generating graphics... => 12
[2,2,1,1,1] generating graphics... => 10
[2,1,1,1,1,1] generating graphics... => 5
[1,1,1,1,1,1,1] generating graphics... => 1
[8] generating graphics... => 22
[7,1] generating graphics... => 23
[6,2] generating graphics... => 49
[6,1,1] generating graphics... => 33
[5,3] generating graphics... => 39
[5,2,1] generating graphics... => 78
[5,1,1,1] generating graphics... => 44
[4,4] generating graphics... => 25
[4,3,1] generating graphics... => 70
[4,2,2] generating graphics... => 67
[4,2,1,1] generating graphics... => 81
[4,1,1,1,1] generating graphics... => 34
[3,3,2] generating graphics... => 35
[3,3,1,1] generating graphics... => 53
[3,2,2,1] generating graphics... => 58
[3,2,1,1,1] generating graphics... => 52
[3,1,1,1,1,1] generating graphics... => 17
[2,2,2,2] generating graphics... => 19
[2,2,2,1,1] generating graphics... => 19
[2,2,1,1,1,1] generating graphics... => 17
[2,1,1,1,1,1,1] generating graphics... => 5
[1,1,1,1,1,1,1,1] generating graphics... => 2
[9] generating graphics... => 30
[8,1] generating graphics... => 37
[7,2] generating graphics... => 79
[7,1,1] generating graphics... => 57
[6,3] generating graphics... => 87
[6,2,1] generating graphics... => 154
[6,1,1,1] generating graphics... => 82
[5,4] generating graphics... => 64
[5,3,1] generating graphics... => 188
[5,2,2] generating graphics... => 152
[5,2,1,1] generating graphics... => 201
[5,1,1,1,1] generating graphics... => 75
[4,4,1] generating graphics... => 95
[4,3,2] generating graphics... => 168
[4,3,1,1] generating graphics... => 207
[4,2,2,1] generating graphics... => 203
[4,2,1,1,1] generating graphics... => 169
[4,1,1,1,1,1] generating graphics... => 52
[3,3,3] generating graphics... => 41
[3,3,2,1] generating graphics... => 144
[3,3,1,1,1] generating graphics... => 104
[3,2,2,2] generating graphics... => 81
[3,2,2,1,1] generating graphics... => 130
[3,2,1,1,1,1] generating graphics... => 84
[3,1,1,1,1,1,1] generating graphics... => 23
[2,2,2,2,1] generating graphics... => 34
[2,2,2,1,1,1] generating graphics... => 39
[2,2,1,1,1,1,1] generating graphics... => 21
[2,1,1,1,1,1,1,1] generating graphics... => 7
[1,1,1,1,1,1,1,1,1] generating graphics... => 2
click to show generating function       
Description
The row sums of the character table of the symmetric group.
Equivalently, this is the multiplicity of the irreducible representation corresponding to the given partition in the adjoint representation of the symmetric group.
Code
def statistic(L):
    G = SymmetricGroup(sum(L))
    rho = SymmetricGroupRepresentation(L)
    chi = rho.to_character()
    return sum( chi(pi) for pi in G.conjugacy_classes_representatives() )

Created
Jun 13, 2013 at 12:58 by Chris Berg
Updated
Apr 17, 2019 at 12:30 by Martin Rubey