***************************************************************************** * 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: St001780 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The order of promotion on the set of standard tableaux of given shape. ----------------------------------------------------------------------------- References: [1] Stanley, R. P. Promotion and evacuation [[MathSciNet:2515772]] ----------------------------------------------------------------------------- Code: def statistic(la): from sage.combinat.cyclic_sieving_phenomenon import orbit_decomposition return lcm(len(o) for o in orbit_decomposition(StandardTableaux(la), lambda T: T.promotion())) ----------------------------------------------------------------------------- Statistic values: [1] => 1 [2] => 1 [1,1] => 1 [3] => 1 [2,1] => 2 [1,1,1] => 1 [4] => 1 [3,1] => 3 [2,2] => 2 [2,1,1] => 3 [1,1,1,1] => 1 [5] => 1 [4,1] => 4 [3,2] => 6 [3,1,1] => 4 [2,2,1] => 6 [2,1,1,1] => 4 [1,1,1,1,1] => 1 [6] => 1 [5,1] => 5 [4,2] => 20 [4,1,1] => 5 [3,3] => 6 [3,2,1] => 12 [3,1,1,1] => 5 [2,2,2] => 6 [2,2,1,1] => 20 [2,1,1,1,1] => 5 [1,1,1,1,1,1] => 1 [7] => 1 [6,1] => 6 [5,2] => 30 [5,1,1] => 6 [4,3] => 8 [4,2,1] => 260 [4,1,1,1] => 6 [3,3,1] => 195 [3,2,2] => 195 [3,2,1,1] => 260 [3,1,1,1,1] => 6 [2,2,2,1] => 8 [2,2,1,1,1] => 30 [2,1,1,1,1,1] => 6 [1,1,1,1,1,1,1] => 1 [8] => 1 [7,1] => 7 [6,2] => 42 [6,1,1] => 7 [5,3] => 560 [5,2,1] => 924 [5,1,1,1] => 7 [4,4] => 8 [4,3,1] => 352 [4,2,2] => 462 [4,2,1,1] => 660 [4,1,1,1,1] => 7 [3,3,2] => 9 [3,3,1,1] => 462 [3,2,2,1] => 352 [3,2,1,1,1] => 924 [3,1,1,1,1,1] => 7 [2,2,2,2] => 8 [2,2,2,1,1] => 560 [2,2,1,1,1,1] => 42 [2,1,1,1,1,1,1] => 7 [1,1,1,1,1,1,1,1] => 1 [9] => 1 [8,1] => 8 [7,2] => 56 [7,1,1] => 8 [6,3] => 312 [6,2,1] => 3696 [6,1,1,1] => 8 [5,4] => 10 [5,3,1] => 26400 [5,2,2] => 1848 [5,2,1,1] => 308154 [5,1,1,1,1] => 8 [4,4,1] => 6188 [4,3,2] => 252 [4,3,1,1] => 32760 [4,2,2,1] => 32760 [4,2,1,1,1] => 308154 [4,1,1,1,1,1] => 8 [3,3,3] => 9 [3,3,2,1] => 252 [3,3,1,1,1] => 1848 [3,2,2,2] => 6188 [3,2,2,1,1] => 26400 [3,2,1,1,1,1] => 3696 [3,1,1,1,1,1,1] => 8 [2,2,2,2,1] => 10 [2,2,2,1,1,1] => 312 [2,2,1,1,1,1,1] => 56 [2,1,1,1,1,1,1,1] => 8 [1,1,1,1,1,1,1,1,1] => 1 [10] => 1 [9,1] => 9 [8,2] => 72 [8,1,1] => 9 [7,3] => 2394 [7,2,1] => 1656 [7,1,1,1] => 9 [6,4] => 5580 [6,3,1] => 1148850 [6,2,2] => 1656 [6,2,1,1] => 64584 [6,1,1,1,1] => 9 [5,5] => 10 [5,4,1] => 885360 [5,3,2] => 6865460 [5,3,1,1] => 50581800 [5,2,2,1] => 118815436 [5,2,1,1,1] => 16744 [5,1,1,1,1,1] => 9 [4,4,2] => 373920 [4,4,1,1] => 9576 [4,3,3] => 24360 [4,3,2,1] => 20 [4,3,1,1,1] => 118815436 [4,2,2,2] => 9576 [4,2,2,1,1] => 50581800 [4,2,1,1,1,1] => 64584 [4,1,1,1,1,1,1] => 9 [3,3,3,1] => 24360 [3,3,2,2] => 373920 [3,3,2,1,1] => 6865460 [3,3,1,1,1,1] => 1656 [3,2,2,2,1] => 885360 [3,2,2,1,1,1] => 1148850 [3,2,1,1,1,1,1] => 1656 [3,1,1,1,1,1,1,1] => 9 [2,2,2,2,2] => 10 [2,2,2,2,1,1] => 5580 [2,2,2,1,1,1,1] => 2394 [2,2,1,1,1,1,1,1] => 72 [2,1,1,1,1,1,1,1,1] => 9 [1,1,1,1,1,1,1,1,1,1] => 1 [11] => 1 [10,1] => 10 [9,2] => 90 [9,1,1] => 10 [8,3] => 520 [8,2,1] => 10980 [8,1,1,1] => 10 [7,4] => 110880 [7,3,1] => 384300 [7,2,2] => 5490 [7,2,1,1] => 3502620 [7,1,1,1,1] => 10 [6,5] => 12 [6,3,2] => 2046431520 [6,2,2,1] => 99795696 [6,2,1,1,1] => 976530456 [6,1,1,1,1,1] => 10 [5,5,1] => 433440 [5,4,1,1] => 1305103800 [5,3,3] => 4444440 [5,2,2,2] => 95940 [5,2,1,1,1,1] => 976530456 [5,1,1,1,1,1,1] => 10 [4,4,3] => 12 [4,4,1,1,1] => 95940 [4,3,3,1] => 7120080 [4,3,1,1,1,1] => 99795696 [4,2,2,2,1] => 1305103800 [4,2,1,1,1,1,1] => 3502620 [4,1,1,1,1,1,1,1] => 10 [3,3,3,2] => 12 [3,3,3,1,1] => 4444440 [3,3,2,1,1,1] => 2046431520 [3,3,1,1,1,1,1] => 5490 [3,2,2,2,2] => 433440 [3,2,2,1,1,1,1] => 384300 [3,2,1,1,1,1,1,1] => 10980 [3,1,1,1,1,1,1,1,1] => 10 [2,2,2,2,2,1] => 12 [2,2,2,2,1,1,1] => 110880 [2,2,2,1,1,1,1,1] => 520 [2,2,1,1,1,1,1,1,1] => 90 [2,1,1,1,1,1,1,1,1,1] => 10 [1,1,1,1,1,1,1,1,1,1,1] => 1 [12] => 1 [11,1] => 11 [10,2] => 110 [10,1,1] => 11 [9,3] => 6732 [9,2,1] => 8580 [9,1,1,1] => 11 [8,4] => 597080 [8,3,1] => 3138564 [8,2,2] => 4290 [8,2,1,1] => 6108960 [8,1,1,1,1] => 11 [7,5] => 1709400 [7,2,2,1] => 981054360 [7,2,1,1,1] => 42762720 [7,1,1,1,1,1] => 11 [6,6] => 12 [6,3,3] => 11492910 [6,2,2,2] => 52360 [6,2,1,1,1,1] => 11662560 [6,1,1,1,1,1,1] => 11 [5,5,2] => 1558378800 [5,5,1,1] => 1247290 [5,4,3] => 16516800 [5,2,1,1,1,1,1] => 42762720 [5,1,1,1,1,1,1,1] => 11 [4,4,4] => 12 [4,4,2,2] => 2970240 [4,4,1,1,1,1] => 52360 [4,3,1,1,1,1,1] => 981054360 [4,2,2,2,2] => 1247290 [4,2,1,1,1,1,1,1] => 6108960 [4,1,1,1,1,1,1,1,1] => 11 [3,3,3,3] => 12 [3,3,3,2,1] => 16516800 [3,3,3,1,1,1] => 11492910 [3,3,2,2,2] => 1558378800 [3,3,1,1,1,1,1,1] => 4290 [3,2,2,1,1,1,1,1] => 3138564 [3,2,1,1,1,1,1,1,1] => 8580 [3,1,1,1,1,1,1,1,1,1] => 11 [2,2,2,2,2,2] => 12 [2,2,2,2,2,1,1] => 1709400 [2,2,2,2,1,1,1,1] => 597080 [2,2,2,1,1,1,1,1,1] => 6732 [2,2,1,1,1,1,1,1,1,1] => 110 [2,1,1,1,1,1,1,1,1,1,1] => 11 [1,1,1,1,1,1,1,1,1,1,1,1] => 1 [13] => 1 [12,1] => 12 [11,2] => 132 [11,1,1] => 12 [10,3] => 2580 [10,2,1] => 25608 [10,1,1,1] => 12 [9,4] => 233244 [9,2,2] => 12804 [9,2,1,1] => 30921660 [9,1,1,1,1] => 12 [8,5] => 521664 [8,1,1,1,1,1] => 12 [7,6] => 14 [7,3,3] => 12307680 [7,2,2,2] => 414348 [7,1,1,1,1,1,1] => 12 [6,6,1] => 17054400 [6,1,1,1,1,1,1,1] => 12 [5,5,1,1,1] => 5012700 [5,2,2,2,2] => 5012700 [5,1,1,1,1,1,1,1,1] => 12 [4,4,1,1,1,1,1] => 414348 [4,2,1,1,1,1,1,1,1] => 30921660 [4,1,1,1,1,1,1,1,1,1] => 12 [3,3,3,1,1,1,1] => 12307680 [3,3,1,1,1,1,1,1,1] => 12804 [3,2,2,2,2,2] => 17054400 [3,2,1,1,1,1,1,1,1,1] => 25608 [3,1,1,1,1,1,1,1,1,1,1] => 12 [2,2,2,2,2,2,1] => 14 [2,2,2,2,2,1,1,1] => 521664 [2,2,2,2,1,1,1,1,1] => 233244 [2,2,2,1,1,1,1,1,1,1] => 2580 [2,2,1,1,1,1,1,1,1,1,1] => 132 [2,1,1,1,1,1,1,1,1,1,1,1] => 12 [1,1,1,1,1,1,1,1,1,1,1,1,1] => 1 [14] => 1 [13,1] => 13 [12,2] => 156 [12,1,1] => 13 [11,3] => 15158 [11,2,1] => 9204 [11,1,1,1] => 13 [10,4] => 59280 [10,2,2] => 9204 [10,2,1,1] => 4197024 [10,1,1,1,1] => 13 [9,5] => 92678040 [9,2,1,1,1] => 96531552 [9,1,1,1,1,1] => 13 [8,2,2,2] => 190164 [8,2,1,1,1,1] => 965315520 [8,1,1,1,1,1,1] => 13 [7,7] => 14 [7,2,1,1,1,1,1] => 163361088 [7,1,1,1,1,1,1,1] => 13 [6,6,1,1] => 9785880 [6,2,2,2,2] => 1613040 [6,2,1,1,1,1,1,1] => 965315520 [6,1,1,1,1,1,1,1,1] => 13 [5,5,4] => 15 [5,5,1,1,1,1] => 1613040 [5,2,1,1,1,1,1,1,1] => 96531552 [5,1,1,1,1,1,1,1,1,1] => 13 [4,4,1,1,1,1,1,1] => 190164 [4,2,2,2,2,2] => 9785880 [4,2,1,1,1,1,1,1,1,1] => 4197024 [4,1,1,1,1,1,1,1,1,1,1] => 13 [3,3,3,3,2] => 15 [3,3,1,1,1,1,1,1,1,1] => 9204 [3,2,1,1,1,1,1,1,1,1,1] => 9204 [3,1,1,1,1,1,1,1,1,1,1,1] => 13 [2,2,2,2,2,2,2] => 14 [2,2,2,2,2,1,1,1,1] => 92678040 [2,2,2,2,1,1,1,1,1,1] => 59280 [2,2,2,1,1,1,1,1,1,1,1] => 15158 [2,2,1,1,1,1,1,1,1,1,1,1] => 156 [2,1,1,1,1,1,1,1,1,1,1,1,1] => 13 [1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1 [15] => 1 [14,1] => 14 [13,2] => 182 [13,1,1] => 14 [12,3] => 2688 [12,2,1] => 51324 [12,1,1,1] => 14 [11,4] => 2902900 [11,2,2] => 25662 [11,2,1,1] => 185176992 [11,1,1,1,1] => 14 [10,5] => 6126120 [10,3,2] => 441621180 [10,1,1,1,1,1] => 14 [9,3,3] => 282898980 [9,2,2,2] => 1316224 [9,1,1,1,1,1,1] => 14 [8,7] => 16 [8,1,1,1,1,1,1,1] => 14 [7,2,2,2,2] => 3558100 [7,1,1,1,1,1,1,1,1] => 14 [6,6,1,1,1] => 61372584 [6,1,1,1,1,1,1,1,1,1] => 14 [5,5,5] => 15 [5,5,1,1,1,1,1] => 3558100 [5,4,3,2,1] => 30 [5,2,2,2,2,2] => 61372584 [5,1,1,1,1,1,1,1,1,1,1] => 14 [4,4,4,3] => 16 [4,4,1,1,1,1,1,1,1] => 1316224 [4,2,1,1,1,1,1,1,1,1,1] => 185176992 [4,1,1,1,1,1,1,1,1,1,1,1] => 14 [3,3,3,3,3] => 15 [3,3,3,1,1,1,1,1,1] => 282898980 [3,3,2,1,1,1,1,1,1,1] => 441621180 [3,3,1,1,1,1,1,1,1,1,1] => 25662 [3,2,1,1,1,1,1,1,1,1,1,1] => 51324 [3,1,1,1,1,1,1,1,1,1,1,1,1] => 14 [2,2,2,2,2,2,2,1] => 16 [2,2,2,2,2,1,1,1,1,1] => 6126120 [2,2,2,2,1,1,1,1,1,1,1] => 2902900 [2,2,2,1,1,1,1,1,1,1,1,1] => 2688 [2,2,1,1,1,1,1,1,1,1,1,1,1] => 182 [2,1,1,1,1,1,1,1,1,1,1,1,1,1] => 14 [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1 [16] => 1 [15,1] => 15 [14,2] => 210 [14,1,1] => 15 [13,3] => 29640 [13,2,1] => 34860 [13,1,1,1] => 15 [12,4] => 3561180 [12,3,1] => 62957160 [12,2,2] => 17430 [12,2,1,1] => 242730180 [12,1,1,1,1] => 15 [11,1,1,1,1,1] => 15 [10,2,2,2] => 271320 [10,1,1,1,1,1,1] => 15 [9,1,1,1,1,1,1,1] => 15 [8,8] => 16 [8,2,2,2,2] => 15615390 [8,1,1,1,1,1,1,1,1] => 15 [7,7,1,1] => 1006335330 [7,1,1,1,1,1,1,1,1,1] => 15 [6,6,1,1,1,1] => 51207660 [6,2,2,2,2,2] => 51207660 [6,1,1,1,1,1,1,1,1,1,1] => 15 [5,5,1,1,1,1,1,1] => 15615390 [5,1,1,1,1,1,1,1,1,1,1,1] => 15 [4,4,4,4] => 16 ----------------------------------------------------------------------------- Created: Mar 23, 2022 at 09:32 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Mar 23, 2022 at 11:22 by Martin Rubey