*****************************************************************************
* www.FindStat.org - The Combinatorial Statistic Finder *
* *
* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
* *
* 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: St000515
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The number of invariant set partitions when acting with a permutation of given cycle type.
-----------------------------------------------------------------------------
References: [1] Bergeron, F., Labelle, G., Leroux, P. Combinatorial species and tree-like structures [[MathSciNet:1629341]]
-----------------------------------------------------------------------------
Code:
def statistic(la):
Partitionspecies = species.PartitionSpecies().cycle_index_series()
return Partitionspecies.count(la)
-----------------------------------------------------------------------------
Statistic values:
[2] => 2
[1,1] => 2
[3] => 2
[2,1] => 3
[1,1,1] => 5
[4] => 3
[3,1] => 3
[2,2] => 7
[2,1,1] => 7
[1,1,1,1] => 15
[5] => 2
[4,1] => 4
[3,2] => 5
[3,1,1] => 7
[2,2,1] => 12
[2,1,1,1] => 20
[1,1,1,1,1] => 52
[6] => 4
[5,1] => 3
[4,2] => 9
[4,1,1] => 9
[3,3] => 8
[3,2,1] => 10
[3,1,1,1] => 20
[2,2,2] => 31
[2,2,1,1] => 31
[2,1,1,1,1] => 67
[1,1,1,1,1,1] => 203
[7] => 2
[6,1] => 5
[5,2] => 5
[5,1,1] => 7
[4,3] => 7
[4,2,1] => 15
[4,1,1,1] => 25
[3,3,1] => 13
[3,2,2] => 19
[3,2,1,1] => 27
[3,1,1,1,1] => 67
[2,2,2,1] => 59
[2,2,1,1,1] => 97
[2,1,1,1,1,1] => 255
[1,1,1,1,1,1,1] => 877
[8] => 4
[7,1] => 3
[6,2] => 11
[6,1,1] => 11
[5,3] => 5
[5,2,1] => 10
[5,1,1,1] => 20
[4,4] => 16
[4,3,1] => 13
[4,2,2] => 38
[4,2,1,1] => 38
[4,1,1,1,1] => 82
[3,3,2] => 21
[3,3,1,1] => 33
[3,2,2,1] => 43
[3,2,1,1,1] => 87
[3,1,1,1,1,1] => 255
[2,2,2,2] => 164
[2,2,2,1,1] => 164
[2,2,1,1,1,1] => 352
[2,1,1,1,1,1,1] => 1080
[1,1,1,1,1,1,1,1] => 4140
[9] => 3
[8,1] => 5
[7,2] => 5
[7,1,1] => 7
[6,3] => 12
[6,2,1] => 18
[6,1,1,1] => 30
[5,4] => 7
[5,3,1] => 10
[5,2,2] => 19
[5,2,1,1] => 27
[5,1,1,1,1] => 67
[4,4,1] => 23
[4,3,2] => 24
[4,3,1,1] => 34
[4,2,2,1] => 71
[4,2,1,1,1] => 117
[4,1,1,1,1,1] => 307
[3,3,3] => 42
[3,3,2,1] => 46
[3,3,1,1,1] => 102
[3,2,2,2] => 90
[3,2,2,1,1] => 128
[3,2,1,1,1,1] => 322
[3,1,1,1,1,1,1] => 1080
[2,2,2,2,1] => 339
[2,2,2,1,1,1] => 549
[2,2,1,1,1,1,1] => 1439
[2,1,1,1,1,1,1,1] => 5017
[1,1,1,1,1,1,1,1,1] => 21147
[10] => 4
[9,1] => 4
[8,2] => 11
[8,1,1] => 11
[7,3] => 5
[7,2,1] => 10
[7,1,1,1] => 20
[6,4] => 15
[6,3,1] => 19
[6,2,2] => 45
[6,2,1,1] => 45
[6,1,1,1,1] => 97
[5,5] => 10
[5,4,1] => 13
[5,3,2] => 15
[5,3,1,1] => 27
[5,2,2,1] => 43
[5,2,1,1,1] => 87
[5,1,1,1,1,1] => 255
[4,4,2] => 55
[4,4,1,1] => 55
[4,3,3] => 29
[4,3,2,1] => 53
[4,3,1,1,1] => 107
[4,2,2,2] => 195
[4,2,2,1,1] => 195
[4,2,1,1,1,1] => 419
[4,1,1,1,1,1,1] => 1283
[3,3,3,1] => 73
[3,3,2,2] => 83
[3,3,2,1,1] => 135
[3,3,1,1,1,1] => 367
[3,2,2,2,1] => 223
[3,2,2,1,1,1] => 449
[3,2,1,1,1,1,1] => 1335
[3,1,1,1,1,1,1,1] => 5017
[2,2,2,2,2] => 999
[2,2,2,2,1,1] => 999
[2,2,2,1,1,1,1] => 2119
[2,2,1,1,1,1,1,1] => 6503
[2,1,1,1,1,1,1,1,1] => 25287
[1,1,1,1,1,1,1,1,1,1] => 115975
[11] => 2
[10,1] => 5
[9,2] => 7
[9,1,1] => 9
[8,3] => 9
[8,2,1] => 18
[8,1,1,1] => 30
[7,4] => 7
[7,3,1] => 10
[7,2,2] => 19
[7,2,1,1] => 27
[7,1,1,1,1] => 67
[6,5] => 9
[6,4,1] => 23
[6,3,2] => 35
[6,3,1,1] => 47
[6,2,2,1] => 83
[6,2,1,1,1] => 137
[6,1,1,1,1,1] => 359
[5,5,1] => 15
[5,4,2] => 24
[5,4,1,1] => 34
[5,3,3] => 21
[5,3,2,1] => 37
[5,3,1,1,1] => 87
[5,2,2,2] => 90
[5,2,2,1,1] => 128
[5,2,1,1,1,1] => 322
[5,1,1,1,1,1,1] => 1080
[4,4,3] => 39
[4,4,2,1] => 98
[4,4,1,1,1] => 162
[4,3,3,1] => 59
[4,3,2,2] => 109
[4,3,2,1,1] => 155
[4,3,1,1,1,1] => 389
[4,2,2,2,1] => 398
[4,2,2,1,1,1] => 646
[4,2,1,1,1,1,1] => 1694
[4,1,1,1,1,1,1,1] => 5894
[3,3,3,2] => 115
[3,3,3,1,1] => 195
[3,3,2,2,1] => 207
[3,3,2,1,1,1] => 469
[3,3,1,1,1,1,1] => 1491
[3,2,2,2,2] => 503
[3,2,2,2,1,1] => 713
[3,2,2,1,1,1,1] => 1791
[3,2,1,1,1,1,1,1] => 6097
[3,1,1,1,1,1,1,1,1] => 25287
[2,2,2,2,2,1] => 2210
[2,2,2,2,1,1,1] => 3530
[2,2,2,1,1,1,1,1] => 9170
[2,2,1,1,1,1,1,1,1] => 32058
[2,1,1,1,1,1,1,1,1,1] => 137122
[1,1,1,1,1,1,1,1,1,1,1] => 678570
[12] => 6
[11,1] => 3
[10,2] => 11
[10,1,1] => 11
[9,3] => 10
[9,2,1] => 13
[9,1,1,1] => 25
[8,4] => 19
[8,3,1] => 16
[8,2,2] => 45
[8,2,1,1] => 45
[8,1,1,1,1] => 97
[7,5] => 5
[7,4,1] => 13
[7,3,2] => 15
[7,3,1,1] => 27
[7,2,2,1] => 43
[7,2,1,1,1] => 87
[7,1,1,1,1,1] => 255
[6,6] => 28
[6,5,1] => 16
[6,4,2] => 56
[6,4,1,1] => 56
[6,3,3] => 58
[6,3,2,1] => 72
[6,3,1,1,1] => 142
[6,2,2,2] => 226
[6,2,2,1,1] => 226
[6,2,1,1,1,1] => 486
[6,1,1,1,1,1,1] => 1486
[5,5,2] => 25
[5,5,1,1] => 37
[5,4,3] => 20
[5,4,2,1] => 53
[5,4,1,1,1] => 107
[5,3,3,1] => 46
[5,3,2,2] => 62
[5,3,2,1,1] => 114
[5,3,1,1,1,1] => 322
[5,2,2,2,1] => 223
[5,2,2,1,1,1] => 449
[5,2,1,1,1,1,1] => 1335
[5,1,1,1,1,1,1,1] => 5017
[4,4,4] => 111
[4,4,3,1] => 78
[4,4,2,2] => 261
[4,4,2,1,1] => 261
[4,4,1,1,1,1] => 561
[4,3,3,2] => 104
[4,3,3,1,1] => 168
[4,3,2,2,1] => 266
[4,3,2,1,1,1] => 536
[4,3,1,1,1,1,1] => 1590
[4,2,2,2,2] => 1163
[4,2,2,2,1,1] => 1163
[4,2,2,1,1,1,1] => 2471
[4,2,1,1,1,1,1,1] => 7583
[4,1,1,1,1,1,1,1,1] => 29427
[3,3,3,3] => 268
[3,3,3,2,1] => 268
[3,3,3,1,1,1] => 634
[3,3,2,2,2] => 406
[3,3,2,2,1,1] => 670
[3,3,2,1,1,1,1] => 1858
[3,3,1,1,1,1,1,1] => 6706
[3,2,2,2,2,1] => 1338
[3,2,2,2,1,1,1] => 2668
[3,2,2,1,1,1,1,1] => 7942
[3,2,1,1,1,1,1,1,1] => 30304
[3,1,1,1,1,1,1,1,1,1] => 137122
[2,2,2,2,2,2] => 6841
[2,2,2,2,2,1,1] => 6841
[2,2,2,2,1,1,1,1] => 14325
[2,2,2,1,1,1,1,1,1] => 43693
[2,2,1,1,1,1,1,1,1,1] => 170689
[2,1,1,1,1,1,1,1,1,1,1] => 794545
[1,1,1,1,1,1,1,1,1,1,1,1] => 4213597
-----------------------------------------------------------------------------
Created: May 26, 2016 at 21:32 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: May 26, 2016 at 21:32 by Martin Rubey