Identifier
Identifier
Values
[2] generating graphics... => 1
[1,1] generating graphics... => 1
[3] generating graphics... => 1
[2,1] generating graphics... => 8
[1,1,1] generating graphics... => 1
[4] generating graphics... => 1
[3,1] generating graphics... => 27
[2,2] generating graphics... => 8
[2,1,1] generating graphics... => 27
[1,1,1,1] generating graphics... => 1
[5] generating graphics... => 1
[4,1] generating graphics... => 64
[3,2] generating graphics... => 125
[3,1,1] generating graphics... => 216
[2,2,1] generating graphics... => 125
[2,1,1,1] generating graphics... => 64
[1,1,1,1,1] generating graphics... => 1
[6] generating graphics... => 1
[5,1] generating graphics... => 125
[4,2] generating graphics... => 729
[4,1,1] generating graphics... => 1000
[3,3] generating graphics... => 125
[3,2,1] generating graphics... => 4096
[3,1,1,1] generating graphics... => 1000
[2,2,2] generating graphics... => 125
[2,2,1,1] generating graphics... => 729
[2,1,1,1,1] generating graphics... => 125
[1,1,1,1,1,1] generating graphics... => 1
[7] generating graphics... => 1
[6,1] generating graphics... => 216
[5,2] generating graphics... => 2744
[5,1,1] generating graphics... => 3375
[4,3] generating graphics... => 2744
[4,2,1] generating graphics... => 42875
[4,1,1,1] generating graphics... => 8000
[3,3,1] generating graphics... => 9261
[3,2,2] generating graphics... => 9261
[3,2,1,1] generating graphics... => 42875
[3,1,1,1,1] generating graphics... => 3375
[2,2,2,1] generating graphics... => 2744
[2,2,1,1,1] generating graphics... => 2744
[2,1,1,1,1,1] generating graphics... => 216
[1,1,1,1,1,1,1] generating graphics... => 1
[8] generating graphics... => 1
[7,1] generating graphics... => 343
[6,2] generating graphics... => 8000
[6,1,1] generating graphics... => 9261
[5,3] generating graphics... => 21952
[5,2,1] generating graphics... => 262144
[5,1,1,1] generating graphics... => 42875
[4,4] generating graphics... => 2744
[4,3,1] generating graphics... => 343000
[4,2,2] generating graphics... => 175616
[4,2,1,1] generating graphics... => 729000
[4,1,1,1,1] generating graphics... => 42875
[3,3,2] generating graphics... => 74088
[3,3,1,1] generating graphics... => 175616
[3,2,2,1] generating graphics... => 343000
[3,2,1,1,1] generating graphics... => 262144
[3,1,1,1,1,1] generating graphics... => 9261
[2,2,2,2] generating graphics... => 2744
[2,2,2,1,1] generating graphics... => 21952
[2,2,1,1,1,1] generating graphics... => 8000
[2,1,1,1,1,1,1] generating graphics... => 343
[1,1,1,1,1,1,1,1] generating graphics... => 1
[9] generating graphics... => 1
[8,1] generating graphics... => 512
[7,2] generating graphics... => 19683
[7,1,1] generating graphics... => 21952
[6,3] generating graphics... => 110592
[6,2,1] generating graphics... => 1157625
[6,1,1,1] generating graphics... => 175616
[5,4] generating graphics... => 74088
[5,3,1] generating graphics... => 4251528
[5,2,2] generating graphics... => 1728000
[5,2,1,1] generating graphics... => 6751269
[5,1,1,1,1] generating graphics... => 343000
[4,4,1] generating graphics... => 592704
[4,3,2] generating graphics... => 4741632
[4,3,1,1] generating graphics... => 10077696
[4,2,2,1] generating graphics... => 10077696
[4,2,1,1,1] generating graphics... => 6751269
[4,1,1,1,1,1] generating graphics... => 175616
[3,3,3] generating graphics... => 74088
[3,3,2,1] generating graphics... => 4741632
[3,3,1,1,1] generating graphics... => 1728000
[3,2,2,2] generating graphics... => 592704
[3,2,2,1,1] generating graphics... => 4251528
[3,2,1,1,1,1] generating graphics... => 1157625
[3,1,1,1,1,1,1] generating graphics... => 21952
[2,2,2,2,1] generating graphics... => 74088
[2,2,2,1,1,1] generating graphics... => 110592
[2,2,1,1,1,1,1] generating graphics... => 19683
[2,1,1,1,1,1,1,1] generating graphics... => 512
[1,1,1,1,1,1,1,1,1] generating graphics... => 1
[10] generating graphics... => 1
[9,1] generating graphics... => 729
[8,2] generating graphics... => 42875
[8,1,1] generating graphics... => 46656
[7,3] generating graphics... => 421875
[7,2,1] generating graphics... => 4096000
[7,1,1,1] generating graphics... => 592704
[6,4] generating graphics... => 729000
[6,3,1] generating graphics... => 31255875
[6,2,2] generating graphics... => 11390625
[6,2,1,1] generating graphics... => 42875000
[6,1,1,1,1] generating graphics... => 2000376
[5,5] generating graphics... => 74088
[5,4,1] generating graphics... => 23887872
[5,3,2] generating graphics... => 91125000
[5,3,1,1] generating graphics... => 182284263
[5,2,2,1] generating graphics... => 144703125
[5,2,1,1,1] generating graphics... => 89915392
[5,1,1,1,1,1] generating graphics... => 2000376
[4,4,2] generating graphics... => 16003008
[4,4,1,1] generating graphics... => 27000000
[4,3,3] generating graphics... => 9261000
[4,3,2,1] generating graphics... => 452984832
[4,3,1,1,1] generating graphics... => 144703125
[4,2,2,2] generating graphics... => 27000000
[4,2,2,1,1] generating graphics... => 182284263
[4,2,1,1,1,1] generating graphics... => 42875000
[4,1,1,1,1,1,1] generating graphics... => 592704
[3,3,3,1] generating graphics... => 9261000
[3,3,2,2] generating graphics... => 16003008
[3,3,2,1,1] generating graphics... => 91125000
[3,3,1,1,1,1] generating graphics... => 11390625
[3,2,2,2,1] generating graphics... => 23887872
[3,2,2,1,1,1] generating graphics... => 31255875
[3,2,1,1,1,1,1] generating graphics... => 4096000
[3,1,1,1,1,1,1,1] generating graphics... => 46656
[2,2,2,2,2] generating graphics... => 74088
[2,2,2,2,1,1] generating graphics... => 729000
[2,2,2,1,1,1,1] generating graphics... => 421875
[2,2,1,1,1,1,1,1] generating graphics... => 42875
[2,1,1,1,1,1,1,1,1] generating graphics... => 729
[1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[11] generating graphics... => 1
[10,1] generating graphics... => 1000
[9,2] generating graphics... => 85184
[9,1,1] generating graphics... => 91125
[8,3] generating graphics... => 1331000
[8,2,1] generating graphics... => 12326391
[8,1,1,1] generating graphics... => 1728000
[7,4] generating graphics... => 4492125
[7,3,1] generating graphics... => 166375000
[7,2,2] generating graphics... => 57066625
[7,2,1,1] generating graphics... => 209584584
[7,1,1,1,1] generating graphics... => 9261000
[6,5] generating graphics... => 2299968
[6,4,1] generating graphics... => 332812557
[6,3,2] generating graphics... => 970299000
[6,3,1,1] generating graphics... => 1869959168
[6,2,2,1] generating graphics... => 1331000000
[6,2,1,1,1] generating graphics... => 788889024
[6,1,1,1,1,1] generating graphics... => 16003008
[5,5,1] generating graphics... => 35937000
[5,4,2] generating graphics... => 970299000
[5,4,1,1] generating graphics... => 1540798875
[5,3,3] generating graphics... => 287496000
[5,2,2,2] generating graphics... => 561515625
[5,2,1,1,1,1] generating graphics... => 788889024
[5,1,1,1,1,1,1] generating graphics... => 9261000
[4,4,3] generating graphics... => 98611128
[4,4,1,1,1] generating graphics... => 561515625
[4,3,3,1] generating graphics... => 1676676672
[4,3,1,1,1,1] generating graphics... => 1331000000
[4,2,2,2,1] generating graphics... => 1540798875
[4,2,2,1,1,1] generating graphics... => 1869959168
[4,2,1,1,1,1,1] generating graphics... => 209584584
[4,1,1,1,1,1,1,1] generating graphics... => 1728000
[3,3,3,2] generating graphics... => 98611128
[3,3,3,1,1] generating graphics... => 287496000
[3,3,2,2,1] generating graphics... => 970299000
[3,3,2,1,1,1] generating graphics... => 970299000
[3,3,1,1,1,1,1] generating graphics... => 57066625
[3,2,2,2,2] generating graphics... => 35937000
[3,2,2,2,1,1] generating graphics... => 332812557
[3,2,2,1,1,1,1] generating graphics... => 166375000
[3,2,1,1,1,1,1,1] generating graphics... => 12326391
[3,1,1,1,1,1,1,1,1] generating graphics... => 91125
[2,2,2,2,2,1] generating graphics... => 2299968
[2,2,2,2,1,1,1] generating graphics... => 4492125
[2,2,2,1,1,1,1,1] generating graphics... => 1331000
[2,2,1,1,1,1,1,1,1] generating graphics... => 85184
[2,1,1,1,1,1,1,1,1,1] generating graphics... => 1000
[1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[12] generating graphics... => 1
[11,1] generating graphics... => 1331
[10,2] generating graphics... => 157464
[10,1,1] generating graphics... => 166375
[9,3] generating graphics... => 3652264
[9,2,1] generating graphics... => 32768000
[9,1,1,1] generating graphics... => 4492125
[8,4] generating graphics... => 20796875
[8,3,1] generating graphics... => 707347971
[8,2,2] generating graphics... => 233744896
[8,2,1,1] generating graphics... => 843908625
[8,1,1,1,1] generating graphics... => 35937000
[7,5] generating graphics... => 26198073
[7,1,1,1,1,1] generating graphics... => 98611128
[6,6] generating graphics... => 2299968
[6,5,1] generating graphics... => 1540798875
[6,1,1,1,1,1,1] generating graphics... => 98611128
[5,1,1,1,1,1,1,1] generating graphics... => 35937000
[4,4,4] generating graphics... => 98611128
[4,2,1,1,1,1,1,1] generating graphics... => 843908625
[4,1,1,1,1,1,1,1,1] generating graphics... => 4492125
[3,3,3,3] generating graphics... => 98611128
[3,3,1,1,1,1,1,1] generating graphics... => 233744896
[3,2,2,2,2,1] generating graphics... => 1540798875
[3,2,2,1,1,1,1,1] generating graphics... => 707347971
[3,2,1,1,1,1,1,1,1] generating graphics... => 32768000
[3,1,1,1,1,1,1,1,1,1] generating graphics... => 166375
[2,2,2,2,2,2] generating graphics... => 2299968
[2,2,2,2,2,1,1] generating graphics... => 26198073
[2,2,2,2,1,1,1,1] generating graphics... => 20796875
[2,2,2,1,1,1,1,1,1] generating graphics... => 3652264
[2,2,1,1,1,1,1,1,1,1] generating graphics... => 157464
[2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 1331
[1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
click to show generating function       
Description
The cube of the number of standard Young tableaux with shape given by the partition.
Code
def statistic(p):
    return StandardTableaux(p).cardinality()^3

Created
Jul 16, 2017 at 18:21 by Martin Rubey
Updated
Jul 16, 2017 at 18:21 by Martin Rubey