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-----------------------------------------------------------------------------
Statistic identifier: St000901
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The cube of the number of standard Young tableaux with shape given by the partition.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(p):
return StandardTableaux(p).cardinality()^3
-----------------------------------------------------------------------------
Statistic values:
[2] => 1
[1,1] => 1
[3] => 1
[2,1] => 8
[1,1,1] => 1
[4] => 1
[3,1] => 27
[2,2] => 8
[2,1,1] => 27
[1,1,1,1] => 1
[5] => 1
[4,1] => 64
[3,2] => 125
[3,1,1] => 216
[2,2,1] => 125
[2,1,1,1] => 64
[1,1,1,1,1] => 1
[6] => 1
[5,1] => 125
[4,2] => 729
[4,1,1] => 1000
[3,3] => 125
[3,2,1] => 4096
[3,1,1,1] => 1000
[2,2,2] => 125
[2,2,1,1] => 729
[2,1,1,1,1] => 125
[1,1,1,1,1,1] => 1
[7] => 1
[6,1] => 216
[5,2] => 2744
[5,1,1] => 3375
[4,3] => 2744
[4,2,1] => 42875
[4,1,1,1] => 8000
[3,3,1] => 9261
[3,2,2] => 9261
[3,2,1,1] => 42875
[3,1,1,1,1] => 3375
[2,2,2,1] => 2744
[2,2,1,1,1] => 2744
[2,1,1,1,1,1] => 216
[1,1,1,1,1,1,1] => 1
[8] => 1
[7,1] => 343
[6,2] => 8000
[6,1,1] => 9261
[5,3] => 21952
[5,2,1] => 262144
[5,1,1,1] => 42875
[4,4] => 2744
[4,3,1] => 343000
[4,2,2] => 175616
[4,2,1,1] => 729000
[4,1,1,1,1] => 42875
[3,3,2] => 74088
[3,3,1,1] => 175616
[3,2,2,1] => 343000
[3,2,1,1,1] => 262144
[3,1,1,1,1,1] => 9261
[2,2,2,2] => 2744
[2,2,2,1,1] => 21952
[2,2,1,1,1,1] => 8000
[2,1,1,1,1,1,1] => 343
[1,1,1,1,1,1,1,1] => 1
[9] => 1
[8,1] => 512
[7,2] => 19683
[7,1,1] => 21952
[6,3] => 110592
[6,2,1] => 1157625
[6,1,1,1] => 175616
[5,4] => 74088
[5,3,1] => 4251528
[5,2,2] => 1728000
[5,2,1,1] => 6751269
[5,1,1,1,1] => 343000
[4,4,1] => 592704
[4,3,2] => 4741632
[4,3,1,1] => 10077696
[4,2,2,1] => 10077696
[4,2,1,1,1] => 6751269
[4,1,1,1,1,1] => 175616
[3,3,3] => 74088
[3,3,2,1] => 4741632
[3,3,1,1,1] => 1728000
[3,2,2,2] => 592704
[3,2,2,1,1] => 4251528
[3,2,1,1,1,1] => 1157625
[3,1,1,1,1,1,1] => 21952
[2,2,2,2,1] => 74088
[2,2,2,1,1,1] => 110592
[2,2,1,1,1,1,1] => 19683
[2,1,1,1,1,1,1,1] => 512
[1,1,1,1,1,1,1,1,1] => 1
[10] => 1
[9,1] => 729
[8,2] => 42875
[8,1,1] => 46656
[7,3] => 421875
[7,2,1] => 4096000
[7,1,1,1] => 592704
[6,4] => 729000
[6,3,1] => 31255875
[6,2,2] => 11390625
[6,2,1,1] => 42875000
[6,1,1,1,1] => 2000376
[5,5] => 74088
[5,4,1] => 23887872
[5,3,2] => 91125000
[5,3,1,1] => 182284263
[5,2,2,1] => 144703125
[5,2,1,1,1] => 89915392
[5,1,1,1,1,1] => 2000376
[4,4,2] => 16003008
[4,4,1,1] => 27000000
[4,3,3] => 9261000
[4,3,2,1] => 452984832
[4,3,1,1,1] => 144703125
[4,2,2,2] => 27000000
[4,2,2,1,1] => 182284263
[4,2,1,1,1,1] => 42875000
[4,1,1,1,1,1,1] => 592704
[3,3,3,1] => 9261000
[3,3,2,2] => 16003008
[3,3,2,1,1] => 91125000
[3,3,1,1,1,1] => 11390625
[3,2,2,2,1] => 23887872
[3,2,2,1,1,1] => 31255875
[3,2,1,1,1,1,1] => 4096000
[3,1,1,1,1,1,1,1] => 46656
[2,2,2,2,2] => 74088
[2,2,2,2,1,1] => 729000
[2,2,2,1,1,1,1] => 421875
[2,2,1,1,1,1,1,1] => 42875
[2,1,1,1,1,1,1,1,1] => 729
[1,1,1,1,1,1,1,1,1,1] => 1
[11] => 1
[10,1] => 1000
[9,2] => 85184
[9,1,1] => 91125
[8,3] => 1331000
[8,2,1] => 12326391
[8,1,1,1] => 1728000
[7,4] => 4492125
[7,3,1] => 166375000
[7,2,2] => 57066625
[7,2,1,1] => 209584584
[7,1,1,1,1] => 9261000
[6,5] => 2299968
[6,4,1] => 332812557
[6,3,2] => 970299000
[6,3,1,1] => 1869959168
[6,2,2,1] => 1331000000
[6,2,1,1,1] => 788889024
[6,1,1,1,1,1] => 16003008
[5,5,1] => 35937000
[5,4,2] => 970299000
[5,4,1,1] => 1540798875
[5,3,3] => 287496000
[5,2,2,2] => 561515625
[5,2,1,1,1,1] => 788889024
[5,1,1,1,1,1,1] => 9261000
[4,4,3] => 98611128
[4,4,1,1,1] => 561515625
[4,3,3,1] => 1676676672
[4,3,1,1,1,1] => 1331000000
[4,2,2,2,1] => 1540798875
[4,2,2,1,1,1] => 1869959168
[4,2,1,1,1,1,1] => 209584584
[4,1,1,1,1,1,1,1] => 1728000
[3,3,3,2] => 98611128
[3,3,3,1,1] => 287496000
[3,3,2,2,1] => 970299000
[3,3,2,1,1,1] => 970299000
[3,3,1,1,1,1,1] => 57066625
[3,2,2,2,2] => 35937000
[3,2,2,2,1,1] => 332812557
[3,2,2,1,1,1,1] => 166375000
[3,2,1,1,1,1,1,1] => 12326391
[3,1,1,1,1,1,1,1,1] => 91125
[2,2,2,2,2,1] => 2299968
[2,2,2,2,1,1,1] => 4492125
[2,2,2,1,1,1,1,1] => 1331000
[2,2,1,1,1,1,1,1,1] => 85184
[2,1,1,1,1,1,1,1,1,1] => 1000
[1,1,1,1,1,1,1,1,1,1,1] => 1
[12] => 1
[11,1] => 1331
[10,2] => 157464
[10,1,1] => 166375
[9,3] => 3652264
[9,2,1] => 32768000
[9,1,1,1] => 4492125
[8,4] => 20796875
[8,3,1] => 707347971
[8,2,2] => 233744896
[8,2,1,1] => 843908625
[8,1,1,1,1] => 35937000
[7,5] => 26198073
[7,1,1,1,1,1] => 98611128
[6,6] => 2299968
[6,5,1] => 1540798875
[6,1,1,1,1,1,1] => 98611128
[5,1,1,1,1,1,1,1] => 35937000
[4,4,4] => 98611128
[4,2,1,1,1,1,1,1] => 843908625
[4,1,1,1,1,1,1,1,1] => 4492125
[3,3,3,3] => 98611128
[3,3,1,1,1,1,1,1] => 233744896
[3,2,2,2,2,1] => 1540798875
[3,2,2,1,1,1,1,1] => 707347971
[3,2,1,1,1,1,1,1,1] => 32768000
[3,1,1,1,1,1,1,1,1,1] => 166375
[2,2,2,2,2,2] => 2299968
[2,2,2,2,2,1,1] => 26198073
[2,2,2,2,1,1,1,1] => 20796875
[2,2,2,1,1,1,1,1,1] => 3652264
[2,2,1,1,1,1,1,1,1,1] => 157464
[2,1,1,1,1,1,1,1,1,1,1] => 1331
[1,1,1,1,1,1,1,1,1,1,1,1] => 1
-----------------------------------------------------------------------------
Created: Jul 16, 2017 at 18:21 by Martin Rubey
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Last Updated: Jul 16, 2017 at 18:21 by Martin Rubey