edit this statistic or download as text // json
Identifier
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