- FindStat

Identifier

St000088: Integer partitions ⟶ ℤ

Values

=>
                            Cc0002;cc-rep
                            
                            
                            

                        []=>1
[1]=>1
[2]=>2
[1,1]=>0
[3]=>3
[2,1]=>1
[1,1,1]=>1
[4]=>5
[3,1]=>2
[2,2]=>3
[2,1,1]=>2
[1,1,1,1]=>1
[5]=>7
[4,1]=>5
[3,2]=>6
[3,1,1]=>5
[2,2,1]=>4
[2,1,1,1]=>3
[1,1,1,1,1]=>1
[6]=>11
[5,1]=>8
[4,2]=>15
[4,1,1]=>10
[3,3]=>4
[3,2,1]=>13
[3,1,1,1]=>10
[2,2,2]=>8
[2,2,1,1]=>5
[2,1,1,1,1]=>4
[1,1,1,1,1,1]=>1
[7]=>15
[6,1]=>15
[5,2]=>26
[5,1,1]=>19
[4,3]=>18
[4,2,1]=>36
[4,1,1,1]=>21
[3,3,1]=>18
[3,2,2]=>22
[3,2,1,1]=>28
[3,1,1,1,1]=>13
[2,2,2,1]=>12
[2,2,1,1,1]=>10
[2,1,1,1,1,1]=>5
[1,1,1,1,1,1,1]=>1
[8]=>22
[7,1]=>23
[6,2]=>49
[6,1,1]=>33
[5,3]=>39
[5,2,1]=>78
[5,1,1,1]=>44
[4,4]=>25
[4,3,1]=>70
[4,2,2]=>67
[4,2,1,1]=>81
[4,1,1,1,1]=>34
[3,3,2]=>35
[3,3,1,1]=>53
[3,2,2,1]=>58
[3,2,1,1,1]=>52
[3,1,1,1,1,1]=>17
[2,2,2,2]=>19
[2,2,2,1,1]=>19
[2,2,1,1,1,1]=>17
[2,1,1,1,1,1,1]=>5
[1,1,1,1,1,1,1,1]=>2
[9]=>30
[8,1]=>37
[7,2]=>79
[7,1,1]=>57
[6,3]=>87
[6,2,1]=>154
[6,1,1,1]=>82
[5,4]=>64
[5,3,1]=>188
[5,2,2]=>152
[5,2,1,1]=>201
[5,1,1,1,1]=>75
[4,4,1]=>95
[4,3,2]=>168
[4,3,1,1]=>207
[4,2,2,1]=>203
[4,2,1,1,1]=>169
[4,1,1,1,1,1]=>52
[3,3,3]=>41
[3,3,2,1]=>144
[3,3,1,1,1]=>104
[3,2,2,2]=>81
[3,2,2,1,1]=>130
[3,2,1,1,1,1]=>84
[3,1,1,1,1,1,1]=>23
[2,2,2,2,1]=>34
[2,2,2,1,1,1]=>39
[2,2,1,1,1,1,1]=>21
[2,1,1,1,1,1,1,1]=>7
[1,1,1,1,1,1,1,1,1]=>2
                    

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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