- FindStat

Identifier

St000901: Integer partitions ⟶ ℤ

Values

=>
                            Cc0002;cc-rep
                            
                            
                            

                        [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
                    

search for individual values

searching the database for the individual values of this statistic

/ search for generating function

searching the database for statistics with the same generating function

click to show known generating functions

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