Identifier
Identifier
Values
[2] generating graphics... => 1
[1,1] generating graphics... => 4
[3] generating graphics... => -1
[2,1] generating graphics... => -4
[1,1,1] generating graphics... => -7
[4] generating graphics... => 2
[3,1] generating graphics... => 4
[2,2] generating graphics... => 6
[2,1,1] generating graphics... => 9
[1,1,1,1] generating graphics... => 12
[5] generating graphics... => -2
[4,1] generating graphics... => -7
[3,2] generating graphics... => -10
[3,1,1] generating graphics... => -11
[2,2,1] generating graphics... => -17
[2,1,1,1] generating graphics... => -19
[1,1,1,1,1] generating graphics... => -19
[6] generating graphics... => 2
[5,1] generating graphics... => 9
[4,2] generating graphics... => 14
[4,1,1] generating graphics... => 22
[3,3] generating graphics... => 15
[3,2,1] generating graphics... => 36
[3,1,1,1] generating graphics... => 26
[2,2,2] generating graphics... => 15
[2,2,1,1] generating graphics... => 42
[2,1,1,1,1] generating graphics... => 34
[1,1,1,1,1,1] generating graphics... => 30
[7] generating graphics... => -2
[6,1] generating graphics... => -11
[5,2] generating graphics... => -22
[5,1,1] generating graphics... => -32
[4,3] generating graphics... => -29
[4,2,1] generating graphics... => -70
[4,1,1,1] generating graphics... => -53
[3,3,1] generating graphics... => -56
[3,2,2] generating graphics... => -48
[3,2,1,1] generating graphics... => -102
[3,1,1,1,1] generating graphics... => -53
[2,2,2,1] generating graphics... => -58
[2,2,1,1,1] generating graphics... => -83
[2,1,1,1,1,1] generating graphics... => -60
[1,1,1,1,1,1,1] generating graphics... => -45
[8] generating graphics... => 3
[7,1] generating graphics... => 12
[6,2] generating graphics... => 36
[6,1,1] generating graphics... => 41
[5,3] generating graphics... => 46
[5,2,1] generating graphics... => 125
[5,1,1,1] generating graphics... => 87
[4,4] generating graphics... => 39
[4,3,1] generating graphics... => 150
[4,2,2] generating graphics... => 127
[4,2,1,1] generating graphics... => 218
[4,1,1,1,1] generating graphics... => 116
[3,3,2] generating graphics... => 98
[3,3,1,1] generating graphics... => 174
[3,2,2,1] generating graphics... => 202
[3,2,1,1,1] generating graphics... => 233
[3,1,1,1,1,1] generating graphics... => 101
[2,2,2,2] generating graphics... => 68
[2,2,2,1,1] generating graphics... => 138
[2,2,1,1,1,1] generating graphics... => 158
[2,1,1,1,1,1,1] generating graphics... => 98
[1,1,1,1,1,1,1,1] generating graphics... => 67
[9] generating graphics... => -4
[8,1] generating graphics... => -15
[7,2] generating graphics... => -48
[7,1,1] generating graphics... => -52
[6,3] generating graphics... => -85
[6,2,1] generating graphics... => -202
[6,1,1,1] generating graphics... => -127
[5,4] generating graphics... => -84
[5,3,1] generating graphics... => -314
[5,2,2] generating graphics... => -260
[5,2,1,1] generating graphics... => -430
[5,1,1,1,1] generating graphics... => -206
[4,4,1] generating graphics... => -200
[4,3,2] generating graphics... => -371
[4,3,1,1] generating graphics... => -537
[4,2,2,1] generating graphics... => -552
[4,2,1,1,1] generating graphics... => -560
[4,1,1,1,1,1] generating graphics... => -231
[3,3,3] generating graphics... => -98
[3,3,2,1] generating graphics... => -472
[3,3,1,1,1] generating graphics... => -430
[3,2,2,2] generating graphics... => -274
[3,2,2,1,1] generating graphics... => -560
[3,2,1,1,1,1] generating graphics... => -484
[3,1,1,1,1,1,1] generating graphics... => -181
[2,2,2,2,1] generating graphics... => -212
[2,2,2,1,1,1] generating graphics... => -300
[2,2,1,1,1,1,1] generating graphics... => -275
[2,1,1,1,1,1,1,1] generating graphics... => -157
[1,1,1,1,1,1,1,1,1] generating graphics... => -97
[10] generating graphics... => 4
[9,1] generating graphics... => 20
[8,2] generating graphics... => 58
[8,1,1] generating graphics... => 71
[7,3] generating graphics... => 140
[7,2,1] generating graphics... => 300
[7,1,1,1] generating graphics... => 176
[6,4] generating graphics... => 157
[6,3,1] generating graphics... => 609
[6,2,2] generating graphics... => 447
[6,2,1,1] generating graphics... => 768
[6,1,1,1,1] generating graphics... => 326
[5,5] generating graphics... => 99
[5,4,1] generating graphics... => 594
[5,3,2] generating graphics... => 956
[5,3,1,1] generating graphics... => 1259
[5,2,2,1] generating graphics... => 1254
[5,2,1,1,1] generating graphics... => 1197
[5,1,1,1,1,1] generating graphics... => 446
[4,4,2] generating graphics... => 548
[4,4,1,1] generating graphics... => 775
[4,3,3] generating graphics... => 485
[4,3,2,1] generating graphics... => 1924
[4,3,1,1,1] generating graphics... => 1514
[4,2,2,2] generating graphics... => 803
[4,2,2,1,1] generating graphics... => 1696
[4,2,1,1,1,1] generating graphics... => 1256
[4,1,1,1,1,1,1] generating graphics... => 436
[3,3,3,1] generating graphics... => 554
[3,3,2,2] generating graphics... => 778
[3,3,2,1,1] generating graphics... => 1452
[3,3,1,1,1,1] generating graphics... => 960
[3,2,2,2,1] generating graphics... => 1041
[3,2,2,1,1,1] generating graphics... => 1322
[3,2,1,1,1,1,1] generating graphics... => 927
[3,1,1,1,1,1,1,1] generating graphics... => 309
[2,2,2,2,2] generating graphics... => 196
[2,2,2,2,1,1] generating graphics... => 539
[2,2,2,1,1,1,1] generating graphics... => 574
[2,2,1,1,1,1,1,1] generating graphics... => 465
[2,1,1,1,1,1,1,1,1] generating graphics... => 242
[1,1,1,1,1,1,1,1,1,1] generating graphics... => 139
[11] generating graphics... => -4
[10,1] generating graphics... => -24
[9,2] generating graphics... => -76
[9,1,1] generating graphics... => -94
[8,3] generating graphics... => -196
[8,2,1] generating graphics... => -428
[8,1,1,1] generating graphics... => -249
[7,4] generating graphics... => -299
[7,3,1] generating graphics... => -1056
[7,2,2] generating graphics... => -739
[7,2,1,1] generating graphics... => -1244
[7,1,1,1,1] generating graphics... => -497
[6,5] generating graphics... => -252
[6,4,1] generating graphics... => -1350
[6,3,2] generating graphics... => -2012
[6,3,1,1] generating graphics... => -2647
[6,2,2,1] generating graphics... => -2462
[6,2,1,1,1] generating graphics... => -2296
[6,1,1,1,1,1] generating graphics... => -765
[5,5,1] generating graphics... => -712
[5,4,2] generating graphics... => -2089
[5,4,1,1] generating graphics... => -2624
[5,3,3] generating graphics... => -1457
[5,3,2,1] generating graphics... => -5397
[5,3,1,1,1] generating graphics... => -3937
[5,2,2,2] generating graphics... => -2046
[5,2,2,1,1] generating graphics... => -4173
[5,2,1,1,1,1] generating graphics... => -2902
[5,1,1,1,1,1,1] generating graphics... => -895
[4,4,3] generating graphics... => -1026
[4,4,2,1] generating graphics... => -3240
[4,4,1,1,1] generating graphics... => -2338
[4,3,3,1] generating graphics... => -2970
[4,3,2,2] generating graphics... => -3503
[4,3,2,1,1] generating graphics... => -6576
[4,3,1,1,1,1] generating graphics... => -3711
[4,2,2,2,1] generating graphics... => -3530
[4,2,2,1,1,1] generating graphics... => -4292
[4,2,1,1,1,1,1] generating graphics... => -2598
[4,1,1,1,1,1,1,1] generating graphics... => -777
[3,3,3,2] generating graphics... => -1338
[3,3,3,1,1] generating graphics... => -1977
[3,3,2,2,1] generating graphics... => -3299
[3,3,2,1,1,1] generating graphics... => -3735
[3,3,1,1,1,1,1] generating graphics... => -1951
[3,2,2,2,2] generating graphics... => -1218
[3,2,2,2,1,1] generating graphics... => -2898
[3,2,2,1,1,1,1] generating graphics... => -2786
[3,2,1,1,1,1,1,1] generating graphics... => -1682
[3,1,1,1,1,1,1,1,1] generating graphics... => -509
[2,2,2,2,2,1] generating graphics... => -738
[2,2,2,2,1,1,1] generating graphics... => -1141
[2,2,2,1,1,1,1,1] generating graphics... => -1047
[2,2,1,1,1,1,1,1,1] generating graphics... => -751
[2,1,1,1,1,1,1,1,1,1] generating graphics... => -367
[1,1,1,1,1,1,1,1,1,1,1] generating graphics... => -195
[12] generating graphics... => 5
[11,1] generating graphics... => 27
[10,2] generating graphics... => 104
[10,1,1] generating graphics... => 115
[9,3] generating graphics... => 268
[9,2,1] generating graphics... => 596
[9,1,1,1] generating graphics... => 351
[8,4] generating graphics... => 507
[8,3,1] generating graphics... => 1670
[8,2,2] generating graphics... => 1195
[8,2,1,1] generating graphics... => 1904
[8,1,1,1,1] generating graphics... => 757
[7,5] generating graphics... => 531
[7,4,1] generating graphics... => 2715
[7,3,2] generating graphics... => 3782
[7,3,1,1] generating graphics... => 4979
[7,2,2,1] generating graphics... => 4434
[7,2,1,1,1] generating graphics... => 4033
[7,1,1,1,1,1] generating graphics... => 1250
[6,6] generating graphics... => 286
[6,5,1] generating graphics... => 2296
[6,4,2] generating graphics... => 5503
[6,4,1,1] generating graphics... => 6567
[6,3,3] generating graphics... => 3443
[6,3,2,1] generating graphics... => 12517
[6,3,1,1,1] generating graphics... => 8914
[6,2,2,2] generating graphics... => 4561
[6,2,2,1,1] generating graphics... => 8883
[6,2,1,1,1,1] generating graphics... => 5986
[6,1,1,1,1,1,1] generating graphics... => 1642
[5,5,2] generating graphics... => 2760
[5,5,1,1] generating graphics... => 3414
[5,4,3] generating graphics... => 4564
[5,4,2,1] generating graphics... => 13338
[5,4,1,1,1] generating graphics... => 8883
[5,3,3,1] generating graphics... => 9874
[5,3,2,2] generating graphics... => 10886
[5,3,2,1,1] generating graphics... => 20110
[5,3,1,1,1,1] generating graphics... => 10472
[5,2,2,2,1] generating graphics... => 9745
[5,2,2,1,1,1] generating graphics... => 11418
[5,2,1,1,1,1,1] generating graphics... => 6402
[5,1,1,1,1,1,1,1] generating graphics... => 1696
[4,4,4] generating graphics... => 1075
[4,4,3,1] generating graphics... => 7188
[4,4,2,2] generating graphics... => 6853
[4,4,2,1,1] generating graphics... => 12097
[4,4,1,1,1,1] generating graphics... => 6171
[4,3,3,2] generating graphics... => 7765
[4,3,3,1,1] generating graphics... => 11574
[4,3,2,2,1] generating graphics... => 16902
[4,3,2,1,1,1] generating graphics... => 18289
[4,3,1,1,1,1,1] generating graphics... => 8222
[4,2,2,2,2] generating graphics... => 4809
[4,2,2,2,1,1] generating graphics... => 10659
[4,2,2,1,1,1,1] generating graphics... => 9729
[4,2,1,1,1,1,1,1] generating graphics... => 5014
[4,1,1,1,1,1,1,1,1] generating graphics... => 1337
[3,3,3,3] generating graphics... => 1408
[3,3,3,2,1] generating graphics... => 6596
[3,3,3,1,1,1] generating graphics... => 5650
[3,3,2,2,2] generating graphics... => 4467
[3,3,2,2,1,1] generating graphics... => 10034
[3,3,2,1,1,1,1] generating graphics... => 8458
[3,3,1,1,1,1,1,1] generating graphics... => 3749
[3,2,2,2,2,1] generating graphics... => 4824
[3,2,2,2,1,1,1] generating graphics... => 6810
[3,2,2,1,1,1,1,1] generating graphics... => 5454
[3,2,1,1,1,1,1,1,1] generating graphics... => 2911
[3,1,1,1,1,1,1,1,1,1] generating graphics... => 814
[2,2,2,2,2,2] generating graphics... => 791
[2,2,2,2,2,1,1] generating graphics... => 1859
[2,2,2,2,1,1,1,1] generating graphics... => 2251
[2,2,2,1,1,1,1,1,1] generating graphics... => 1804
[2,2,1,1,1,1,1,1,1,1] generating graphics... => 1187
[2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 541
[1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 272
click to show generating function       
Description
The alternating sum of the coefficients of the character polynomial of an integer partition.
The definition of the character polynomial can be found in [1].
References
[1] Garsia, A. M., Goupil, A. Character polynomials, their $q$-analogs and the Kronecker product MathSciNet:2576382
Code
def statistic(L):
    return L.character_polynomial()(*[-1]*sum(L))

Created
Aug 07, 2017 at 14:00 by Christian Stump
Updated
Aug 07, 2017 at 14:00 by Christian Stump