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Statistic identifier: St000944
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Collection: Integer partitions
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Description: The 3-degree of an integer partition.
For an integer partition $\lambda$, this is given by the exponent of 3 in the Gram determinant of the integal Specht module of the symmetric group indexed by $\lambda$.
This stupid comment should not be accepted as an edit!
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References: [1] [[noreference given]]
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Code:
def statistic(L):
return L.prime_degree(12)
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Statistic values:
[1] => 0
[2] => 0
[1,1] => 0
[3] => 1
[2,1] => 1
[1,1,1] => 0
[4] => 1
[3,1] => 0
[2,2] => 1
[2,1,1] => 0
[1,1,1,1] => 0
[5] => 1
[4,1] => 4
[3,2] => 1
[3,1,1] => 0
[2,2,1] => 4
[2,1,1,1] => 0
[1,1,1,1,1] => 0
[6] => 2
[5,1] => 9
[4,2] => 0
[4,1,1] => 16
[3,3] => 6
[3,2,1] => 16
[3,1,1,1] => 4
[2,2,2] => 4
[2,2,1,1] => 0
[2,1,1,1,1] => 1
[1,1,1,1,1,1] => 0
[7] => 2
[6,1] => 6
[5,2] => 27
[5,1,1] => 15
[4,3] => 15
[4,2,1] => 42
[4,1,1,1] => 20
[3,3,1] => 6
[3,2,2] => 15
[3,2,1,1] => 28
[3,1,1,1,1] => 0
[2,2,2,1] => 13
[2,2,1,1,1] => 1
[2,1,1,1,1,1] => 0
[1,1,1,1,1,1,1] => 0
[8] => 2
[7,1] => 14
[6,2] => 33
[6,1,1] => 21
[5,3] => 56
[5,2,1] => 99
[5,1,1,1] => 35
[4,4] => 15
[4,3,1] => 49
[4,2,2] => 78
[4,2,1,1] => 0
[4,1,1,1,1] => 35
[3,3,2] => 21
[3,3,1,1] => 34
[3,2,2,1] => 91
[3,2,1,1,1] => 29
[3,1,1,1,1,1] => 0
[2,2,2,2] => 13
[2,2,2,1,1] => 0
[2,2,1,1,1,1] => 7
[2,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1] => 0
[9] => 3
[8,1] => 23
[7,2] => 27
[7,1,1] => 77
[6,3] => 137
[6,2,1] => 238
[6,1,1,1] => 91
[5,4] => 85
[5,3,1] => 0
[5,2,2] => 233
[5,2,1,1] => 189
[5,1,1,1,1] => 105
[4,4,1] => 134
[4,3,2] => 232
[4,3,1,1] => 27
[4,2,2,1] => 189
[4,2,1,1,1] => 0
[4,1,1,1,1,1] => 77
[3,3,3] => 63
[3,3,2,1] => 272
[3,3,1,1,1] => 127
[3,2,2,2] => 118
[3,2,2,1,1] => 0
[3,2,1,1,1,1] => 77
[3,1,1,1,1,1,1] => 7
[2,2,2,2,1] => 41
[2,2,2,1,1,1] => 7
[2,2,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1] => 0
[10] => 4
[9,1] => 18
[8,2] => 138
[8,1,1] => 72
[7,3] => 191
[7,2,1] => 496
[7,1,1,1] => 168
[6,4] => 180
[6,3,1] => 594
[6,2,2] => 351
[6,2,1,1] => 1064
[6,1,1,1,1] => 126
[5,5] => 85
[5,4,1] => 297
[5,3,2] => 297
[5,3,1,1] => 0
[5,2,2,1] => 1232
[5,2,1,1,1] => 896
[5,1,1,1,1,1] => 126
[4,4,2] => 198
[4,4,1,1] => 593
[4,3,3] => 463
[4,3,2,1] => 1152
[4,3,1,1,1] => 343
[4,2,2,2] => 307
[4,2,2,1,1] => 0
[4,2,1,1,1,1] => 336
[4,1,1,1,1,1,1] => 84
[3,3,3,1] => 167
[3,3,2,2] => 306
[3,3,2,1,1] => 603
[3,3,1,1,1,1] => 99
[3,2,2,2,1] => 279
[3,2,2,1,1,1] => 36
[3,2,1,1,1,1,1] => 144
[3,1,1,1,1,1,1,1] => 0
[2,2,2,2,2] => 41
[2,2,2,2,1,1] => 0
[2,2,2,1,1,1,1] => 34
[2,2,1,1,1,1,1,1] => 2
[2,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1] => 0
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Created: Aug 22, 2017 at 01:24 by Martin Rubey
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Last Updated: Aug 22, 2017 at 10:43 by Christian Stump