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

Created
Aug 11, 2017 at 17:05 by Christian Stump
Updated
Aug 11, 2017 at 17:05 by Christian Stump