***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew * * * * This information is distributed in the hope that it will be useful, * * but WITHOUT ANY WARRANTY; without even the implied warranty of * * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * ***************************************************************************** ----------------------------------------------------------------------------- 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 ----------------------------------------------------------------------------- Last Updated: Jul 16, 2017 at 18:21 by Martin Rubey