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Statistic identifier: St000934
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The 2-degree of an integer partition.
For an integer partition $\lambda$, this is given by the exponent of 2 in the Gram determinant of the integal Specht module of the symmetric group indexed by $\lambda$.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(L):
return L.prime_degree(2)
-----------------------------------------------------------------------------
Statistic values:
[2] => 1
[1,1] => 0
[3] => 1
[2,1] => 0
[1,1,1] => 0
[4] => 2
[3,1] => 5
[2,2] => 2
[2,1,1] => 1
[1,1,1,1] => 0
[5] => 3
[4,1] => 4
[3,2] => 14
[3,1,1] => 6
[2,2,1] => 1
[2,1,1,1] => 0
[1,1,1,1,1] => 0
[6] => 4
[5,1] => 19
[4,2] => 27
[4,1,1] => 16
[3,3] => 14
[3,2,1] => 0
[3,1,1,1] => 14
[2,2,2] => 6
[2,2,1,1] => 9
[2,1,1,1,1] => 1
[1,1,1,1,1,1] => 0
[7] => 4
[6,1] => 18
[5,2] => 42
[5,1,1] => 45
[4,3] => 36
[4,2,1] => 97
[4,1,1,1] => 20
[3,3,1] => 62
[3,2,2] => 22
[3,2,1,1] => 43
[3,1,1,1,1] => 15
[2,2,2,1] => 6
[2,2,1,1,1] => 0
[2,1,1,1,1,1] => 0
[1,1,1,1,1,1,1] => 0
[8] => 6
[7,1] => 40
[6,2] => 94
[6,1,1] => 93
[5,3] => 106
[5,2,1] => 64
[5,1,1,1] => 145
[4,4] => 64
[4,3,1] => 342
[4,2,2] => 154
[4,2,1,1] => 270
[4,1,1,1,1] => 65
[3,3,2] => 126
[3,3,1,1] => 70
[3,2,2,1] => 78
[3,2,1,1,1] => 0
[3,1,1,1,1,1] => 33
[2,2,2,2] => 20
[2,2,2,1,1] => 34
[2,2,1,1,1,1] => 6
[2,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1] => 0
[9] => 7
[8,1] => 32
[7,2] => 187
[7,1,1] => 112
[6,3] => 144
[6,2,1] => 629
[6,1,1,1] => 168
[5,4] => 226
[5,3,1] => 704
[5,2,2] => 282
[5,2,1,1] => 659
[5,1,1,1,1] => 210
[4,4,1] => 266
[4,3,2] => 664
[4,3,1,1] => 592
[4,2,2,1] => 272
[4,2,1,1,1] => 664
[4,1,1,1,1,1] => 56
[3,3,3] => 126
[3,3,2,1] => 8
[3,3,1,1,1] => 198
[3,2,2,2] => 154
[3,2,2,1,1] => 268
[3,2,1,1,1,1] => 106
[3,1,1,1,1,1,1] => 28
[2,2,2,2,1] => 26
[2,2,2,1,1,1] => 0
[2,2,1,1,1,1,1] => 2
[2,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1] => 0
[10] => 8
[9,1] => 71
[8,2] => 254
[8,1,1] => 172
[7,3] => 571
[7,2,1] => 480
[7,1,1,1] => 392
[6,4] => 508
[6,3,1] => 2116
[6,2,2] => 1496
[6,2,1,1] => 1568
[6,1,1,1,1] => 448
[5,5] => 226
[5,4,1] => 704
[5,3,2] => 2436
[5,3,1,1] => 2630
[5,2,2,1] => 1888
[5,2,1,1,1] => 448
[5,1,1,1,1,1] => 434
[4,4,2] => 1182
[4,4,1,1] => 1074
[4,3,3] => 832
[4,3,2,1] => 0
[4,3,1,1,1] => 2312
[4,2,2,2] => 726
[4,2,2,1,1] => 1906
[4,2,1,1,1,1] => 882
[4,1,1,1,1,1,1] => 112
[3,3,3,1] => 638
[3,3,2,2] => 330
[3,3,2,1,1] => 714
[3,3,1,1,1,1] => 304
[3,2,2,2,1] => 160
[3,2,2,1,1,1] => 404
[3,2,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1] => 44
[2,2,2,2,2] => 68
[2,2,2,2,1,1] => 122
[2,2,2,1,1,1,1] => 29
[2,2,1,1,1,1,1,1] => 26
[2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1] => 0
[11] => 8
[10,1] => 70
[9,2] => 264
[9,1,1] => 315
[8,3] => 750
[8,2,1] => 1670
[8,1,1,1] => 480
[7,4] => 1319
[7,3,1] => 3332
[7,2,2] => 2136
[7,2,1,1] => 2608
[7,1,1,1,1] => 840
[6,5] => 692
[6,4,1] => 4138
[6,3,2] => 6588
[6,3,1,1] => 3696
[6,2,2,1] => 3552
[6,2,1,1,1] => 4004
[6,1,1,1,1,1] => 756
[5,5,1] => 1794
[5,4,2] => 5312
[5,4,1,1] => 5575
[5,3,3] => 3058
[5,3,2,1] => 10188
[5,3,1,1,1] => 5236
[5,2,2,2] => 3739
[5,2,2,1,1] => 4004
[5,2,1,1,1,1] => 1540
[5,1,1,1,1,1,1] => 630
[4,4,3] => 1804
[4,4,2,1] => 5028
[4,4,1,1,1] => 2861
[4,3,3,1] => 3564
[4,3,2,2] => 1572
[4,3,2,1,1] => 5982
[4,3,1,1,1,1] => 3048
[4,2,2,2,1] => 3665
[4,2,2,1,1,1] => 1232
[4,2,1,1,1,1,1] => 1550
[4,1,1,1,1,1,1,1] => 120
[3,3,3,2] => 1430
[3,3,3,1,1] => 902
[3,3,2,2,1] => 1618
[3,3,2,1,1,1] => 342
[3,3,1,1,1,1,1] => 944
[3,2,2,2,2] => 516
[3,2,2,2,1,1] => 1406
[3,2,2,1,1,1,1] => 518
[3,2,1,1,1,1,1,1] => 178
[3,1,1,1,1,1,1,1,1] => 45
[2,2,2,2,2,1] => 100
[2,2,2,2,1,1,1] => 1
[2,2,2,1,1,1,1,1] => 20
[2,2,1,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1,1] => 0
[12] => 10
[11,1] => 108
[10,2] => 476
[10,1,1] => 475
[9,3] => 1234
[9,2,1] => 1280
[9,1,1,1] => 1395
[8,4] => 2619
[8,3,1] => 8095
[8,2,2] => 3652
[8,2,1,1] => 6780
[8,1,1,1,1] => 1740
[7,5] => 2539
[7,4,1] => 4224
[7,3,2] => 15961
[7,3,1,1] => 12738
[7,2,2,1] => 12102
[7,2,1,1,1] => 5184
[7,1,1,1,1,1] => 2352
[6,6] => 824
[6,5,1] => 9693
[6,4,2] => 20691
[6,4,1,1] => 13486
[6,3,3] => 11626
[6,3,2,1] => 5632
[6,3,1,1,1] => 14784
[6,2,2,2] => 10041
[6,2,2,1,1] => 16488
[6,2,1,1,1,1] => 8400
[6,1,1,1,1,1,1] => 1806
[5,5,2] => 6446
[5,5,1,1] => 8524
[5,4,3] => 8128
[5,4,2,1] => 40788
[5,4,1,1,1] => 8832
[5,3,3,1] => 27304
[5,3,2,2] => 24409
[5,3,2,1,1] => 30800
[5,3,1,1,1,1] => 12024
[5,2,2,2,1] => 5248
[5,2,2,1,1,1] => 7392
[5,2,1,1,1,1,1] => 1728
[5,1,1,1,1,1,1,1] => 1230
[4,4,4] => 2728
[4,4,3,1] => 16732
[4,4,2,2] => 7920
[4,4,2,1,1] => 20141
[4,4,1,1,1,1] => 9209
[4,3,3,2] => 9998
[4,3,3,1,1] => 10118
[4,3,2,2,1] => 16962
[4,3,2,1,1,1] => 0
[4,3,1,1,1,1,1] => 8688
[4,2,2,2,2] => 6326
[4,2,2,2,1,1] => 8074
[4,2,2,1,1,1,1] => 3894
[4,2,1,1,1,1,1,1] => 2670
[4,1,1,1,1,1,1,1,1] => 255
[3,3,3,3] => 1430
[3,3,3,2,1] => 320
[3,3,3,1,1,1] => 3224
[3,3,2,2,2] => 2794
[3,3,2,2,1,1] => 6039
[3,3,2,1,1,1,1] => 3289
[3,3,1,1,1,1,1,1] => 660
[3,2,2,2,2,1] => 1857
[3,2,2,2,1,1,1] => 0
[3,2,2,1,1,1,1,1] => 815
[3,2,1,1,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1,1,1] => 75
[2,2,2,2,2,2] => 232
[2,2,2,2,2,1,1] => 431
[2,2,2,2,1,1,1,1] => 131
[2,2,2,1,1,1,1,1,1] => 152
[2,2,1,1,1,1,1,1,1,1] => 10
[2,1,1,1,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,1,1,1,1,1,1,1] => 0
-----------------------------------------------------------------------------
Created: Aug 11, 2017 at 17:05 by Christian Stump
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Last Updated: Aug 11, 2017 at 17:05 by Christian Stump