Identifier
Identifier
Values
[] generating graphics... => 1
[1] generating graphics... => 1
[2] generating graphics... => 1
[1,1] generating graphics... => 0
[3] generating graphics... => 1
[2,1] generating graphics... => 1
[1,1,1] generating graphics... => 0
[4] generating graphics... => 1
[3,1] generating graphics... => 1
[2,2] generating graphics... => 1
[2,1,1] generating graphics... => 1
[1,1,1,1] generating graphics... => 0
[5] generating graphics... => 1
[4,1] generating graphics... => 1
[3,2] generating graphics... => 1
[3,1,1] generating graphics... => 1
[2,2,1] generating graphics... => 1
[2,1,1,1] generating graphics... => 0
[1,1,1,1,1] generating graphics... => 0
[6] generating graphics... => 1
[5,1] generating graphics... => 1
[4,2] generating graphics... => 2
[4,1,1] generating graphics... => 1
[3,3] generating graphics... => 0
[3,2,1] generating graphics... => 5
[3,1,1,1] generating graphics... => 1
[2,2,2] generating graphics... => 1
[2,2,1,1] generating graphics... => 0
[2,1,1,1,1] generating graphics... => 0
[1,1,1,1,1,1] generating graphics... => 0
[7] generating graphics... => 1
[6,1] generating graphics... => 1
[5,2] generating graphics... => 2
[5,1,1] generating graphics... => 1
[4,3] generating graphics... => 1
[4,2,1] generating graphics... => 9
[4,1,1,1] generating graphics... => 1
[3,3,1] generating graphics... => 1
[3,2,2] generating graphics... => 2
[3,2,1,1] generating graphics... => 8
[3,1,1,1,1] generating graphics... => 1
[2,2,2,1] generating graphics... => 1
[2,2,1,1,1] generating graphics... => 0
[2,1,1,1,1,1] generating graphics... => 0
[1,1,1,1,1,1,1] generating graphics... => 0
[8] generating graphics... => 1
[7,1] generating graphics... => 1
[6,2] generating graphics... => 2
[6,1,1] generating graphics... => 1
[5,3] generating graphics... => 1
[5,2,1] generating graphics... => 9
[5,1,1,1] generating graphics... => 1
[4,4] generating graphics... => 1
[4,3,1] generating graphics... => 8
[4,2,2] generating graphics... => 6
[4,2,1,1] generating graphics... => 17
[4,1,1,1,1] generating graphics... => 1
[3,3,2] generating graphics... => 1
[3,3,1,1] generating graphics... => 5
[3,2,2,1] generating graphics... => 8
[3,2,1,1,1] generating graphics... => 4
[3,1,1,1,1,1] generating graphics... => 0
[2,2,2,2] generating graphics... => 1
[2,2,2,1,1] generating graphics... => 0
[2,2,1,1,1,1] generating graphics... => 0
[2,1,1,1,1,1,1] generating graphics... => 0
[1,1,1,1,1,1,1,1] generating graphics... => 0
[9] generating graphics... => 1
[8,1] generating graphics... => 1
[7,2] generating graphics... => 2
[7,1,1] generating graphics... => 1
[6,3] generating graphics... => 2
[6,2,1] generating graphics... => 9
[6,1,1,1] generating graphics... => 1
[5,4] generating graphics... => 1
[5,3,1] generating graphics... => 15
[5,2,2] generating graphics... => 7
[5,2,1,1] generating graphics... => 18
[5,1,1,1,1] generating graphics... => 1
[4,4,1] generating graphics... => 2
[4,3,2] generating graphics... => 12
[4,3,1,1] generating graphics... => 27
[4,2,2,1] generating graphics... => 28
[4,2,1,1,1] generating graphics... => 17
[4,1,1,1,1,1] generating graphics... => 1
[3,3,3] generating graphics... => 1
[3,3,2,1] generating graphics... => 11
[3,3,1,1,1] generating graphics... => 5
[3,2,2,2] generating graphics... => 2
[3,2,2,1,1] generating graphics... => 7
[3,2,1,1,1,1] generating graphics... => 0
[3,1,1,1,1,1,1] generating graphics... => 0
[2,2,2,2,1] generating graphics... => 0
[2,2,2,1,1,1] generating graphics... => 0
[2,2,1,1,1,1,1] generating graphics... => 0
[2,1,1,1,1,1,1,1] generating graphics... => 0
[1,1,1,1,1,1,1,1,1] generating graphics... => 0
[10] generating graphics... => 1
[9,1] generating graphics... => 1
[8,2] generating graphics... => 2
[8,1,1] generating graphics... => 1
[7,3] generating graphics... => 2
[7,2,1] generating graphics... => 9
[7,1,1,1] generating graphics... => 1
[6,4] generating graphics... => 2
[6,3,1] generating graphics... => 19
[6,2,2] generating graphics... => 7
[6,2,1,1] generating graphics... => 18
[6,1,1,1,1] generating graphics... => 1
[5,5] generating graphics... => 0
[5,4,1] generating graphics... => 9
[5,3,2] generating graphics... => 29
[5,3,1,1] generating graphics... => 53
[5,2,2,1] generating graphics... => 39
[5,2,1,1,1] generating graphics... => 21
[5,1,1,1,1,1] generating graphics... => 1
[4,4,2] generating graphics... => 6
[4,4,1,1] generating graphics... => 5
[4,3,3] generating graphics... => 2
[4,3,2,1] generating graphics... => 117
[4,3,1,1,1] generating graphics... => 40
[4,2,2,2] generating graphics... => 10
[4,2,2,1,1] generating graphics... => 46
[4,2,1,1,1,1] generating graphics... => 11
[4,1,1,1,1,1,1] generating graphics... => 1
[3,3,3,1] generating graphics... => 2
[3,3,2,2] generating graphics... => 2
[3,3,2,1,1] generating graphics... => 21
[3,3,1,1,1,1] generating graphics... => 1
[3,2,2,2,1] generating graphics... => 5
[3,2,2,1,1,1] generating graphics... => 1
[3,2,1,1,1,1,1] generating graphics... => 0
[3,1,1,1,1,1,1,1] generating graphics... => 0
[2,2,2,2,2] generating graphics... => 0
[2,2,2,2,1,1] generating graphics... => 0
[2,2,2,1,1,1,1] generating graphics... => 0
[2,2,1,1,1,1,1,1] generating graphics... => 0
[2,1,1,1,1,1,1,1,1] generating graphics... => 0
[1,1,1,1,1,1,1,1,1,1] generating graphics... => 0
[11] generating graphics... => 1
[10,1] generating graphics... => 1
[9,2] generating graphics... => 2
[9,1,1] generating graphics... => 1
[8,3] generating graphics... => 2
[8,2,1] generating graphics... => 9
[8,1,1,1] generating graphics... => 1
[7,4] generating graphics... => 2
[7,3,1] generating graphics... => 19
[7,2,2] generating graphics... => 7
[7,2,1,1] generating graphics... => 18
[7,1,1,1,1] generating graphics... => 1
[6,5] generating graphics... => 1
[6,4,1] generating graphics... => 19
[6,3,2] generating graphics... => 39
[6,3,1,1] generating graphics... => 62
[6,2,2,1] generating graphics... => 39
[6,2,1,1,1] generating graphics... => 21
[6,1,1,1,1,1] generating graphics... => 1
[5,5,1] generating graphics... => 1
[5,4,2] generating graphics... => 29
[5,4,1,1] generating graphics... => 40
[5,3,3] generating graphics... => 6
[5,3,2,1] generating graphics... => 312
[5,3,1,1,1] generating graphics... => 89
[5,2,2,2] generating graphics... => 17
[5,2,2,1,1] generating graphics... => 86
[5,2,1,1,1,1] generating graphics... => 20
[5,1,1,1,1,1,1] generating graphics... => 1
[4,4,3] generating graphics... => 2
[4,4,2,1] generating graphics... => 53
[4,4,1,1,1] generating graphics... => 14
[4,3,3,1] generating graphics... => 37
[4,3,2,2] generating graphics... => 53
[4,3,2,1,1] generating graphics... => 301
[4,3,1,1,1,1] generating graphics... => 30
[4,2,2,2,1] generating graphics... => 37
[4,2,2,1,1,1] generating graphics... => 32
[4,2,1,1,1,1,1] generating graphics... => 4
[4,1,1,1,1,1,1,1] generating graphics... => 0
[3,3,3,2] generating graphics... => 2
[3,3,3,1,1] generating graphics... => 8
[3,3,2,2,1] generating graphics... => 21
[3,3,2,1,1,1] generating graphics... => 11
[3,3,1,1,1,1,1] generating graphics... => 0
[3,2,2,2,2] generating graphics... => 1
[3,2,2,2,1,1] generating graphics... => 1
[3,2,2,1,1,1,1] generating graphics... => 0
[3,2,1,1,1,1,1,1] generating graphics... => 0
[3,1,1,1,1,1,1,1,1] generating graphics... => 0
[2,2,2,2,2,1] generating graphics... => 0
[2,2,2,2,1,1,1] generating graphics... => 0
[2,2,2,1,1,1,1,1] generating graphics... => 0
[2,2,1,1,1,1,1,1,1] generating graphics... => 0
[2,1,1,1,1,1,1,1,1,1] generating graphics... => 0
[1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 0
[12] generating graphics... => 1
[11,1] generating graphics... => 1
[10,2] generating graphics... => 2
[10,1,1] generating graphics... => 1
[9,3] generating graphics... => 2
[9,2,1] generating graphics... => 9
[9,1,1,1] generating graphics... => 1
[8,4] generating graphics... => 3
[8,3,1] generating graphics... => 19
[8,2,2] generating graphics... => 7
[8,2,1,1] generating graphics... => 18
[8,1,1,1,1] generating graphics... => 1
[7,5] generating graphics... => 1
[7,4,1] generating graphics... => 26
[7,3,2] generating graphics... => 40
[7,3,1,1] generating graphics... => 63
[7,2,2,1] generating graphics... => 39
[7,2,1,1,1] generating graphics... => 21
[7,1,1,1,1,1] generating graphics... => 1
[6,6] generating graphics... => 1
[6,5,1] generating graphics... => 9
[6,4,2] generating graphics... => 71
[6,4,1,1] generating graphics... => 80
[6,3,3] generating graphics... => 13
[6,3,2,1] generating graphics... => 429
[6,3,1,1,1] generating graphics... => 108
[6,2,2,2] generating graphics... => 19
[6,2,2,1,1] generating graphics... => 90
[6,2,1,1,1,1] generating graphics... => 21
[6,1,1,1,1,1,1] generating graphics... => 1
[5,5,2] generating graphics... => 5
[5,5,1,1] generating graphics... => 9
[5,4,3] generating graphics... => 20
[5,4,2,1] generating graphics... => 407
[5,4,1,1,1] generating graphics... => 89
[5,3,3,1] generating graphics... => 146
[5,3,2,2] generating graphics... => 179
[5,3,2,1,1] generating graphics... => 945
[5,3,1,1,1,1] generating graphics... => 91
[5,2,2,2,1] generating graphics... => 94
[5,2,2,1,1,1] generating graphics... => 103
[5,2,1,1,1,1,1] generating graphics... => 17
[5,1,1,1,1,1,1,1] generating graphics... => 1
[4,4,4] generating graphics... => 2
[4,4,3,1] generating graphics... => 46
[4,4,2,2] generating graphics... => 45
[4,4,2,1,1] generating graphics... => 180
[4,4,1,1,1,1] generating graphics... => 18
[4,3,3,2] generating graphics... => 47
[4,3,3,1,1] generating graphics... => 144
[4,3,2,2,1] generating graphics... => 380
[4,3,2,1,1,1] generating graphics... => 312
[4,3,1,1,1,1,1] generating graphics... => 11
[4,2,2,2,2] generating graphics... => 9
[4,2,2,2,1,1] generating graphics... => 35
[4,2,2,1,1,1,1] generating graphics... => 10
[4,2,1,1,1,1,1,1] generating graphics... => 0
[4,1,1,1,1,1,1,1,1] generating graphics... => 0
[3,3,3,3] generating graphics... => 1
[3,3,3,2,1] generating graphics... => 15
[3,3,3,1,1,1] generating graphics... => 7
[3,3,2,2,2] generating graphics... => 4
[3,3,2,2,1,1] generating graphics... => 21
[3,3,2,1,1,1,1] generating graphics... => 0
[3,3,1,1,1,1,1,1] generating graphics... => 0
[3,2,2,2,2,1] generating graphics... => 0
[3,2,2,2,1,1,1] generating graphics... => 0
[3,2,2,1,1,1,1,1] generating graphics... => 0
[3,2,1,1,1,1,1,1,1] generating graphics... => 0
[3,1,1,1,1,1,1,1,1,1] generating graphics... => 0
[2,2,2,2,2,2] generating graphics... => 0
[2,2,2,2,2,1,1] generating graphics... => 0
[2,2,2,2,1,1,1,1] generating graphics... => 0
[2,2,2,1,1,1,1,1,1] generating graphics... => 0
[2,2,1,1,1,1,1,1,1,1] generating graphics... => 0
[2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 0
[1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 0
[5,4,3,1] generating graphics... => 523
[5,4,2,2] generating graphics... => 333
[5,4,2,1,1] generating graphics... => 1573
[5,3,3,2] generating graphics... => 232
[5,3,3,1,1] generating graphics... => 661
[5,3,2,2,1] generating graphics... => 1580
[4,4,3,2] generating graphics... => 85
[4,4,3,1,1] generating graphics... => 235
[4,4,2,2,1] generating graphics... => 325
[4,3,3,2,1] generating graphics... => 494
[5,4,3,2] generating graphics... => 1169
[5,4,3,1,1] generating graphics... => 2929
[5,4,2,2,1] generating graphics... => 3649
[5,3,3,2,1] generating graphics... => 2933
[4,4,3,2,1] generating graphics... => 1154
[5,4,3,2,1] generating graphics... => 18269
click to show generating function       
Description
The multiplicity of the irreducible representation indexed by the partition in the Kronecker square corresponding to the partition.
The Kronecker coefficient is the multiplicity $g_{\mu,\nu}^\lambda$ of the Specht module $S^\lambda$ in $S^\mu\otimes S^\nu$:
$$ S^\mu\otimes S^\nu = \bigoplus_\lambda g_{\mu,\nu}^\lambda S^\lambda $$
This statistic records the Kronecker coefficient $g_{\lambda,\lambda}^\lambda$.
Code
def statistic(la):
    s = SymmetricFunctions(ZZ).schur()
    return s[la].internal_product(s[la]).coefficient(la)

Created
Mar 17, 2018 at 10:22 by Martin Rubey
Updated
Mar 17, 2018 at 10:29 by Martin Rubey