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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
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* This information is distributed in the hope that it will be useful, *
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
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-----------------------------------------------------------------------------
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