*****************************************************************************
* 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: St001606
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on set partitions.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(mu):
s = SymmetricFunctions(QQ).s()
F = species.PartitionSpecies().cycle_index_series()
return F.coefficient(mu.size()).scalar(s(mu))
-----------------------------------------------------------------------------
Statistic values:
[1] => 1
[2] => 2
[1,1] => 0
[3] => 3
[2,1] => 1
[1,1,1] => 0
[4] => 5
[3,1] => 2
[2,2] => 2
[2,1,1] => 0
[1,1,1,1] => 0
[5] => 7
[4,1] => 5
[3,2] => 4
[3,1,1] => 0
[2,2,1] => 1
[2,1,1,1] => 0
[1,1,1,1,1] => 0
[6] => 11
[5,1] => 8
[4,2] => 10
[4,1,1] => 1
[3,3] => 2
[3,2,1] => 2
[3,1,1,1] => 0
[2,2,2] => 2
[2,2,1,1] => 0
[2,1,1,1,1] => 0
[1,1,1,1,1,1] => 0
[7] => 15
[6,1] => 15
[5,2] => 17
[5,1,1] => 2
[4,3] => 10
[4,2,1] => 7
[4,1,1,1] => 0
[3,3,1] => 1
[3,2,2] => 4
[3,2,1,1] => 0
[3,1,1,1,1] => 0
[2,2,2,1] => 1
[2,2,1,1,1] => 0
[2,1,1,1,1,1] => 0
[1,1,1,1,1,1,1] => 0
[8] => 22
[7,1] => 23
[6,2] => 32
[6,1,1] => 5
[5,3] => 20
[5,2,1] => 14
[5,1,1,1] => 0
[4,4] => 12
[4,3,1] => 9
[4,2,2] => 11
[4,2,1,1] => 1
[4,1,1,1,1] => 0
[3,3,2] => 2
[3,3,1,1] => 0
[3,2,2,1] => 2
[3,2,1,1,1] => 0
[3,1,1,1,1,1] => 0
[2,2,2,2] => 2
[2,2,2,1,1] => 0
[2,2,1,1,1,1] => 0
[2,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1] => 0
[9] => 30
[8,1] => 37
[7,2] => 51
[7,1,1] => 10
[6,3] => 44
[6,2,1] => 29
[6,1,1,1] => 0
[5,4] => 27
[5,3,1] => 22
[5,2,2] => 22
[5,2,1,1] => 3
[5,1,1,1,1] => 0
[4,4,1] => 15
[4,3,2] => 14
[4,3,1,1] => 2
[4,2,2,1] => 7
[4,2,1,1,1] => 0
[4,1,1,1,1,1] => 0
[3,3,3] => 0
[3,3,2,1] => 1
[3,3,1,1,1] => 0
[3,2,2,2] => 4
[3,2,2,1,1] => 0
[3,2,1,1,1,1] => 0
[3,1,1,1,1,1,1] => 0
[2,2,2,2,1] => 1
[2,2,2,1,1,1] => 0
[2,2,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1] => 0
[10] => 42
[9,1] => 55
[8,2] => 84
[8,1,1] => 18
[7,3] => 76
[7,2,1] => 53
[7,1,1,1] => 1
[6,4] => 66
[6,3,1] => 53
[6,2,2] => 44
[6,2,1,1] => 7
[6,1,1,1,1] => 0
[5,5] => 16
[5,4,1] => 39
[5,3,2] => 36
[5,3,1,1] => 8
[5,2,2,1] => 16
[5,2,1,1,1] => 0
[5,1,1,1,1,1] => 0
[4,4,2] => 25
[4,4,1,1] => 5
[4,3,3] => 5
[4,3,2,1] => 10
[4,3,1,1,1] => 0
[4,2,2,2] => 11
[4,2,2,1,1] => 1
[4,2,1,1,1,1] => 0
[4,1,1,1,1,1,1] => 0
[3,3,3,1] => 0
[3,3,2,2] => 2
[3,3,2,1,1] => 0
[3,3,1,1,1,1] => 0
[3,2,2,2,1] => 2
[3,2,2,1,1,1] => 0
[3,2,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1] => 0
[2,2,2,2,2] => 2
[2,2,2,2,1,1] => 0
[2,2,2,1,1,1,1] => 0
[2,2,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1] => 0
[11] => 56
[10,1] => 83
[9,2] => 128
[9,1,1] => 31
[8,3] => 134
[8,2,1] => 94
[8,1,1,1] => 2
[7,4] => 121
[7,3,1] => 105
[7,2,2] => 78
[7,2,1,1] => 17
[7,1,1,1,1] => 0
[6,5] => 67
[6,4,1] => 101
[6,3,2] => 88
[6,3,1,1] => 20
[6,2,2,1] => 35
[6,2,1,1,1] => 0
[6,1,1,1,1,1] => 0
[5,5,1] => 28
[5,4,2] => 70
[5,4,1,1] => 19
[5,3,3] => 17
[5,3,2,1] => 32
[5,3,1,1,1] => 1
[5,2,2,2] => 23
[5,2,2,1,1] => 3
[5,2,1,1,1,1] => 0
[5,1,1,1,1,1,1] => 0
[4,4,3] => 22
[4,4,2,1] => 21
[4,4,1,1,1] => 0
[4,3,3,1] => 4
[4,3,2,2] => 14
[4,3,2,1,1] => 2
[4,3,1,1,1,1] => 0
[4,2,2,2,1] => 7
[4,2,2,1,1,1] => 0
[4,2,1,1,1,1,1] => 0
[4,1,1,1,1,1,1,1] => 0
[3,3,3,2] => 0
[3,3,3,1,1] => 0
[3,3,2,2,1] => 1
[3,3,2,1,1,1] => 0
[3,3,1,1,1,1,1] => 0
[3,2,2,2,2] => 4
[3,2,2,2,1,1] => 0
[3,2,2,1,1,1,1] => 0
[3,2,1,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1,1] => 0
[2,2,2,2,2,1] => 1
[2,2,2,2,1,1,1] => 0
[2,2,2,1,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1,1] => 0
[12] => 77
[11,1] => 118
[10,2] => 197
[10,1,1] => 52
[9,3] => 216
[9,2,1] => 156
[9,1,1,1] => 5
[8,4] => 223
[8,3,1] => 198
[8,2,2] => 139
[8,2,1,1] => 34
[8,1,1,1,1] => 0
[7,5] => 144
[7,4,1] => 208
[7,3,2] => 176
[7,3,1,1] => 50
[7,2,2,1] => 68
[7,2,1,1,1] => 1
[7,1,1,1,1,1] => 0
[6,6] => 68
[6,5,1] => 118
[6,4,2] => 186
[6,4,1,1] => 51
[6,3,3] => 52
[6,3,2,1] => 83
[6,3,1,1,1] => 2
[6,2,2,2] => 49
[6,2,2,1,1] => 8
[6,2,1,1,1,1] => 0
[6,1,1,1,1,1,1] => 0
[5,5,2] => 55
[5,5,1,1] => 20
[5,4,3] => 66
[5,4,2,1] => 73
[5,4,1,1,1] => 3
[5,3,3,1] => 20
[5,3,2,2] => 40
[5,3,2,1,1] => 10
[5,3,1,1,1,1] => 0
[5,2,2,2,1] => 16
[5,2,2,1,1,1] => 0
[5,2,1,1,1,1,1] => 0
[5,1,1,1,1,1,1,1] => 0
[4,4,4] => 24
[4,4,3,1] => 22
[4,4,2,2] => 27
[4,4,2,1,1] => 5
[4,4,1,1,1,1] => 0
[4,3,3,2] => 5
[4,3,3,1,1] => 1
[4,3,2,2,1] => 10
[4,3,2,1,1,1] => 0
[4,3,1,1,1,1,1] => 0
[4,2,2,2,2] => 11
[4,2,2,2,1,1] => 1
[4,2,2,1,1,1,1] => 0
[4,2,1,1,1,1,1,1] => 0
[4,1,1,1,1,1,1,1,1] => 0
[3,3,3,3] => 0
[3,3,3,2,1] => 0
[3,3,3,1,1,1] => 0
[3,3,2,2,2] => 2
[3,3,2,2,1,1] => 0
[3,3,2,1,1,1,1] => 0
[3,3,1,1,1,1,1,1] => 0
[3,2,2,2,2,1] => 2
[3,2,2,2,1,1,1] => 0
[3,2,2,1,1,1,1,1] => 0
[3,2,1,1,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1,1,1] => 0
[2,2,2,2,2,2] => 2
[2,2,2,2,2,1,1] => 0
[2,2,2,2,1,1,1,1] => 0
[2,2,2,1,1,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1,1,1] => 0
[13] => 101
[12,1] => 171
[11,2] => 288
[11,1,1] => 82
[10,3] => 347
[10,2,1] => 256
[10,1,1,1] => 10
[9,4] => 372
[9,3,1] => 347
[9,2,2] => 229
[9,2,1,1] => 65
[9,1,1,1,1] => 0
[8,5] => 297
[8,4,1] => 406
[8,3,2] => 341
[8,3,1,1] => 103
[8,2,2,1] => 130
[8,2,1,1,1] => 3
[8,1,1,1,1,1] => 0
[7,6] => 176
[7,5,1] => 287
[7,4,2] => 391
[7,4,1,1] => 126
[7,3,3] => 119
[7,3,2,1] => 185
[7,3,1,1,1] => 8
[7,2,2,2] => 90
[7,2,2,1,1] => 19
[7,2,1,1,1,1] => 0
[7,1,1,1,1,1,1] => 0
[6,6,1] => 127
[6,5,2] => 234
[6,5,1,1] => 75
[6,4,3] => 194
[6,4,2,1] => 204
[6,4,1,1,1] => 8
[6,3,3,1] => 62
[6,3,2,2] => 106
[6,3,2,1,1] => 28
[6,3,1,1,1,1] => 0
[6,2,2,2,1] => 37
[6,2,2,1,1,1] => 0
[6,2,1,1,1,1,1] => 0
[6,1,1,1,1,1,1,1] => 0
[5,5,3] => 59
[5,5,2,1] => 73
[5,5,1,1,1] => 7
[5,4,4] => 68
[5,4,3,1] => 88
[5,4,2,2] => 89
[5,4,2,1,1] => 27
[5,4,1,1,1,1] => 0
[5,3,3,2] => 23
[5,3,3,1,1] => 10
[5,3,2,2,1] => 33
[5,3,2,1,1,1] => 1
[5,3,1,1,1,1,1] => 0
[5,2,2,2,2] => 23
[5,2,2,2,1,1] => 3
[5,2,2,1,1,1,1] => 0
[5,2,1,1,1,1,1,1] => 0
[5,1,1,1,1,1,1,1,1] => 0
[4,4,4,1] => 30
[4,4,3,2] => 30
[4,4,3,1,1] => 6
[4,4,2,2,1] => 21
[4,4,2,1,1,1] => 0
[4,4,1,1,1,1,1] => 0
[4,3,3,3] => 0
[4,3,3,2,1] => 4
[4,3,3,1,1,1] => 0
[4,3,2,2,2] => 14
[4,3,2,2,1,1] => 2
[4,3,2,1,1,1,1] => 0
[4,3,1,1,1,1,1,1] => 0
[4,2,2,2,2,1] => 7
[4,2,2,2,1,1,1] => 0
[4,2,2,1,1,1,1,1] => 0
[4,2,1,1,1,1,1,1,1] => 0
[4,1,1,1,1,1,1,1,1,1] => 0
[3,3,3,3,1] => 0
[3,3,3,2,2] => 0
[3,3,3,2,1,1] => 0
[3,3,3,1,1,1,1] => 0
[3,3,2,2,2,1] => 1
[3,3,2,2,1,1,1] => 0
[3,3,2,1,1,1,1,1] => 0
[3,3,1,1,1,1,1,1,1] => 0
[3,2,2,2,2,2] => 4
[3,2,2,2,2,1,1] => 0
[3,2,2,2,1,1,1,1] => 0
[3,2,2,1,1,1,1,1,1] => 0
[3,2,1,1,1,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1,1,1,1] => 0
[2,2,2,2,2,2,1] => 1
[2,2,2,2,2,1,1,1] => 0
[2,2,2,2,1,1,1,1,1] => 0
[2,2,2,1,1,1,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[14] => 135
[13,1] => 238
[12,2] => 424
[12,1,1] => 127
[11,3] => 528
[11,2,1] => 401
[11,1,1,1] => 20
[10,4] => 616
[10,3,1] => 591
[10,2,2] => 376
[10,2,1,1] => 117
[10,1,1,1,1] => 0
[9,5] => 531
[9,4,1] => 729
[9,3,2] => 607
[9,3,1,1] => 203
[9,2,2,1] => 230
[9,2,1,1,1] => 8
[9,1,1,1,1,1] => 0
[8,6] => 404
[8,5,1] => 622
[8,4,2] => 787
[8,4,1,1] => 266
[8,3,3] => 250
[8,3,2,1] => 382
[8,3,1,1,1] => 20
[8,2,2,2] => 168
[8,2,2,1,1] => 41
[8,2,1,1,1,1] => 0
[8,1,1,1,1,1,1] => 0
[7,7] => 122
[7,6,1] => 383
[7,5,2] => 581
[7,5,1,1] => 215
[7,4,3] => 440
[7,4,2,1] => 474
[7,4,1,1,1] => 28
[7,3,3,1] => 161
[7,3,2,2] => 227
[7,3,2,1,1] => 73
[7,3,1,1,1,1] => 0
[7,2,2,2,1] => 74
[7,2,2,1,1,1] => 1
[7,2,1,1,1,1,1] => 0
[7,1,1,1,1,1,1,1] => 0
[6,6,2] => 262
[6,6,1,1] => 80
[6,5,3] => 286
[6,5,2,1] => 299
[6,5,1,1,1] => 20
[6,4,4] => 197
[6,4,3,1] => 270
[6,4,2,2] => 257
[6,4,2,1,1] => 82
[6,4,1,1,1,1] => 0
[6,3,3,2] => 79
[6,3,3,1,1] => 31
[6,3,2,2,1] => 93
[6,3,2,1,1,1] => 3
[6,3,1,1,1,1,1] => 0
[6,2,2,2,2] => 50
[6,2,2,2,1,1] => 8
[6,2,2,1,1,1,1] => 0
[6,2,1,1,1,1,1,1] => 0
[6,1,1,1,1,1,1,1,1] => 0
[5,5,4] => 64
[5,5,3,1] => 105
[5,5,2,2] => 86
[5,5,2,1,1] => 40
[5,5,1,1,1,1] => 1
[5,4,4,1] => 107
[5,4,3,2] => 118
[5,4,3,1,1] => 44
[5,4,2,2,1] => 80
[5,4,2,1,1,1] => 3
[5,4,1,1,1,1,1] => 0
[5,3,3,3] => 4
[5,3,3,2,1] => 24
[5,3,3,1,1,1] => 2
[5,3,2,2,2] => 40
[5,3,2,2,1,1] => 10
[5,3,2,1,1,1,1] => 0
[5,3,1,1,1,1,1,1] => 0
[5,2,2,2,2,1] => 16
[5,2,2,2,1,1,1] => 0
[5,2,2,1,1,1,1,1] => 0
[5,2,1,1,1,1,1,1,1] => 0
[5,1,1,1,1,1,1,1,1,1] => 0
[4,4,4,2] => 47
[4,4,4,1,1] => 10
[4,4,3,3] => 10
[4,4,3,2,1] => 24
[4,4,3,1,1,1] => 0
[4,4,2,2,2] => 27
[4,4,2,2,1,1] => 5
[4,4,2,1,1,1,1] => 0
[4,4,1,1,1,1,1,1] => 0
[4,3,3,3,1] => 0
[4,3,3,2,2] => 5
[4,3,3,2,1,1] => 1
[4,3,3,1,1,1,1] => 0
[4,3,2,2,2,1] => 10
[4,3,2,2,1,1,1] => 0
[4,3,2,1,1,1,1,1] => 0
[4,3,1,1,1,1,1,1,1] => 0
[4,2,2,2,2,2] => 11
[4,2,2,2,2,1,1] => 1
[4,2,2,2,1,1,1,1] => 0
[4,2,2,1,1,1,1,1,1] => 0
[4,2,1,1,1,1,1,1,1,1] => 0
[4,1,1,1,1,1,1,1,1,1,1] => 0
[3,3,3,3,2] => 0
[3,3,3,3,1,1] => 0
[3,3,3,2,2,1] => 0
[3,3,3,2,1,1,1] => 0
[3,3,3,1,1,1,1,1] => 0
[3,3,2,2,2,2] => 2
[3,3,2,2,2,1,1] => 0
[3,3,2,2,1,1,1,1] => 0
[3,3,2,1,1,1,1,1,1] => 0
[3,3,1,1,1,1,1,1,1,1] => 0
[3,2,2,2,2,2,1] => 2
[3,2,2,2,2,1,1,1] => 0
[3,2,2,2,1,1,1,1,1] => 0
[3,2,2,1,1,1,1,1,1,1] => 0
[3,2,1,1,1,1,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1,1,1,1,1] => 0
[2,2,2,2,2,2,2] => 2
[2,2,2,2,2,2,1,1] => 0
[2,2,2,2,2,1,1,1,1] => 0
[2,2,2,2,1,1,1,1,1,1] => 0
[2,2,2,1,1,1,1,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[15] => 176
[14,1] => 332
[13,2] => 603
[13,1,1] => 193
[12,3] => 803
[12,2,1] => 619
[12,1,1,1] => 34
[11,4] => 962
[11,3,1] => 960
[11,2,2] => 591
[11,2,1,1] => 204
[11,1,1,1,1] => 1
[10,5] => 928
[10,4,1] => 1271
[10,3,2] => 1052
[10,3,1,1] => 373
[10,2,2,1] => 399
[10,2,1,1,1] => 17
[10,1,1,1,1,1] => 0
[9,6] => 767
[9,5,1] => 1194
[9,4,2] => 1444
[9,4,1,1] => 529
[9,3,3] => 484
[9,3,2,1] => 729
[9,3,1,1,1] => 47
[9,2,2,2] => 290
[9,2,2,1,1] => 83
[9,2,1,1,1,1] => 0
[9,1,1,1,1,1,1] => 0
[8,7] => 416
[8,6,1] => 927
[8,5,2] => 1300
[8,5,1,1] => 493
[8,4,3] => 931
[8,4,2,1] => 1013
[8,4,1,1,1] => 69
[8,3,3,1] => 359
[8,3,2,2] => 471
[8,3,2,1,1] => 166
[8,3,1,1,1,1] => 1
[8,2,2,2,1] => 145
[8,2,2,1,1,1] => 3
[8,2,1,1,1,1,1] => 0
[8,1,1,1,1,1,1,1] => 0
[7,7,1] => 312
[7,6,2] => 814
[7,6,1,1] => 309
[7,5,3] => 771
[7,5,2,1] => 814
[7,5,1,1,1] => 70
[7,4,4] => 447
[7,4,3,1] => 680
[7,4,2,2] => 585
[7,4,2,1,1] => 221
[7,4,1,1,1,1] => 1
[7,3,3,2] => 208
[7,3,3,1,1] => 90
[7,3,2,2,1] => 216
[7,3,2,1,1,1] => 10
[7,3,1,1,1,1,1] => 0
[7,2,2,2,2] => 95
[7,2,2,2,1,1] => 20
[7,2,2,1,1,1,1] => 0
[7,2,1,1,1,1,1,1] => 0
[7,1,1,1,1,1,1,1,1] => 0
[6,6,3] => 366
[6,6,2,1] => 339
[6,6,1,1,1] => 18
[6,5,4] => 336
[6,5,3,1] => 471
[6,5,2,2] => 379
[6,5,2,1,1] => 154
[6,5,1,1,1,1] => 2
[6,4,4,1] => 329
[6,4,3,2] => 383
[6,4,3,1,1] => 145
[6,4,2,2,1] => 246
[6,4,2,1,1,1] => 11
[6,4,1,1,1,1,1] => 0
[6,3,3,3] => 20
[6,3,3,2,1] => 84
[6,3,3,1,1,1] => 8
[6,3,2,2,2] => 110
[6,3,2,2,1,1] => 30
[6,3,2,1,1,1,1] => 0
[6,3,1,1,1,1,1,1] => 0
[6,2,2,2,2,1] => 37
[6,2,2,2,1,1,1] => 0
[6,2,2,1,1,1,1,1] => 0
[6,2,1,1,1,1,1,1,1] => 0
[6,1,1,1,1,1,1,1,1,1] => 0
[5,5,5] => 20
[5,5,4,1] => 136
[5,5,3,2] => 144
[5,5,3,1,1] => 79
[5,5,2,2,1] => 92
[5,5,2,1,1,1] => 10
[5,5,1,1,1,1,1] => 0
[5,4,4,2] => 170
[5,4,4,1,1] => 59
[5,4,3,3] => 52
[5,4,3,2,1] => 122
[5,4,3,1,1,1] => 8
[5,4,2,2,2] => 91
[5,4,2,2,1,1] => 27
[5,4,2,1,1,1,1] => 0
[5,4,1,1,1,1,1,1] => 0
[5,3,3,3,1] => 6
[5,3,3,2,2] => 23
[5,3,3,2,1,1] => 11
[5,3,3,1,1,1,1] => 0
[5,3,2,2,2,1] => 33
[5,3,2,2,1,1,1] => 1
[5,3,2,1,1,1,1,1] => 0
[5,3,1,1,1,1,1,1,1] => 0
[5,2,2,2,2,2] => 23
[5,2,2,2,2,1,1] => 3
[5,2,2,2,1,1,1,1] => 0
[5,2,2,1,1,1,1,1,1] => 0
[5,2,1,1,1,1,1,1,1,1] => 0
[5,1,1,1,1,1,1,1,1,1,1] => 0
[4,4,4,3] => 38
[4,4,4,2,1] => 40
[4,4,4,1,1,1] => 0
[4,4,3,3,1] => 8
[4,4,3,2,2] => 30
[4,4,3,2,1,1] => 6
[4,4,3,1,1,1,1] => 0
[4,4,2,2,2,1] => 21
[4,4,2,2,1,1,1] => 0
[4,4,2,1,1,1,1,1] => 0
[4,4,1,1,1,1,1,1,1] => 0
[4,3,3,3,2] => 0
[4,3,3,3,1,1] => 0
[4,3,3,2,2,1] => 4
[4,3,3,2,1,1,1] => 0
[4,3,3,1,1,1,1,1] => 0
[4,3,2,2,2,2] => 14
[4,3,2,2,2,1,1] => 2
[4,3,2,2,1,1,1,1] => 0
[4,3,2,1,1,1,1,1,1] => 0
[4,3,1,1,1,1,1,1,1,1] => 0
[4,2,2,2,2,2,1] => 7
[4,2,2,2,2,1,1,1] => 0
[4,2,2,2,1,1,1,1,1] => 0
[4,2,2,1,1,1,1,1,1,1] => 0
[4,2,1,1,1,1,1,1,1,1,1] => 0
[4,1,1,1,1,1,1,1,1,1,1,1] => 0
[3,3,3,3,3] => 0
[3,3,3,3,2,1] => 0
[3,3,3,3,1,1,1] => 0
[3,3,3,2,2,2] => 0
[3,3,3,2,2,1,1] => 0
[3,3,3,2,1,1,1,1] => 0
[3,3,3,1,1,1,1,1,1] => 0
[3,3,2,2,2,2,1] => 1
[3,3,2,2,2,1,1,1] => 0
[3,3,2,2,1,1,1,1,1] => 0
[3,3,2,1,1,1,1,1,1,1] => 0
[3,3,1,1,1,1,1,1,1,1,1] => 0
[3,2,2,2,2,2,2] => 4
[3,2,2,2,2,2,1,1] => 0
[3,2,2,2,2,1,1,1,1] => 0
[3,2,2,2,1,1,1,1,1,1] => 0
[3,2,2,1,1,1,1,1,1,1,1] => 0
[3,2,1,1,1,1,1,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[2,2,2,2,2,2,2,1] => 1
[2,2,2,2,2,2,1,1,1] => 0
[2,2,2,2,2,1,1,1,1,1] => 0
[2,2,2,2,1,1,1,1,1,1,1] => 0
[2,2,2,1,1,1,1,1,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[16] => 231
[15,1] => 453
[14,2] => 857
[14,1,1] => 285
[13,3] => 1178
[13,2,1] => 932
[13,1,1,1] => 60
[12,4] => 1496
[12,3,1] => 1526
[12,2,2] => 919
[12,2,1,1] => 338
[12,1,1,1,1] => 2
[11,5] => 1512
[11,4,1] => 2105
[11,3,2] => 1740
[11,3,1,1] => 662
[11,2,2,1] => 663
[11,2,1,1,1] => 37
[11,1,1,1,1,1] => 0
[10,6] => 1401
[10,5,1] => 2189
[10,4,2] => 2571
[10,4,1,1] => 986
[10,3,3] => 885
[10,3,2,1] => 1332
[10,3,1,1,1] => 97
[10,2,2,2] => 497
[10,2,2,1,1] => 157
[10,2,1,1,1,1] => 0
[10,1,1,1,1,1,1] => 0
[9,7] => 915
[9,6,1] => 1893
[9,5,2] => 2557
[9,5,1,1] => 1034
[9,4,3] => 1800
[9,4,2,1] => 1988
[9,4,1,1,1] => 161
[9,3,3,1] => 743
[9,3,2,2] => 891
[9,3,2,1,1] => 350
[9,3,1,1,1,1] => 3
[9,2,2,2,1] => 267
[9,2,2,1,1,1] => 9
[9,2,1,1,1,1,1] => 0
[9,1,1,1,1,1,1,1] => 0
[8,8] => 363
[8,7,1] => 1067
[8,6,2] => 2043
[8,6,1,1] => 803
[8,5,3] => 1815
[8,5,2,1] => 1909
[8,5,1,1,1] => 176
[8,4,4] => 958
[8,4,3,1] => 1526
[8,4,2,2] => 1267
[8,4,2,1,1] => 516
[8,4,1,1,1,1] => 5
[8,3,3,2] => 483
[8,3,3,1,1] => 218
[8,3,2,2,1] => 470
[8,3,2,1,1,1] => 28
[8,3,1,1,1,1,1] => 0
[8,2,2,2,2] => 180
[8,2,2,2,1,1] => 43
[8,2,2,1,1,1,1] => 0
[8,2,1,1,1,1,1,1] => 0
[8,1,1,1,1,1,1,1,1] => 0
[7,7,2] => 692
[7,7,1,1] => 312
[7,6,3] => 1220
[7,6,2,1] => 1208
[7,6,1,1,1] => 107
[7,5,4] => 944
[7,5,3,1] => 1384
[7,5,2,2] => 1015
[7,5,2,1,1] => 469
[7,5,1,1,1,1] => 8
[7,4,4,1] => 817
[7,4,3,2] => 979
[7,4,3,1,1] => 417
[7,4,2,2,1] => 606
[7,4,2,1,1,1] => 39
[7,4,1,1,1,1,1] => 0
[7,3,3,3] => 73
[7,3,3,2,1] => 236
[7,3,3,1,1,1] => 23
[7,3,2,2,2] => 245
[7,3,2,2,1,1] => 81
[7,3,2,1,1,1,1] => 0
[7,3,1,1,1,1,1,1] => 0
[7,2,2,2,2,1] => 76
[7,2,2,2,1,1,1] => 1
[7,2,2,1,1,1,1,1] => 0
[7,2,1,1,1,1,1,1,1] => 0
[7,1,1,1,1,1,1,1,1,1] => 0
[6,6,4] => 490
[6,6,3,1] => 602
[6,6,2,2] => 452
[6,6,2,1,1] => 173
[6,6,1,1,1,1] => 1
[6,5,5] => 178
[6,5,4,1] => 665
[6,5,3,2] => 702
[6,5,3,1,1] => 324
[6,5,2,2,1] => 410
[6,5,2,1,1,1] => 35
[6,5,1,1,1,1,1] => 0
[6,4,4,2] => 542
[6,4,4,1,1] => 202
[6,4,3,3] => 190
[6,4,3,2,1] => 422
[6,4,3,1,1,1] => 34
[6,4,2,2,2] => 278
[6,4,2,2,1,1] => 90
[6,4,2,1,1,1,1] => 0
[6,4,1,1,1,1,1,1] => 0
[6,3,3,3,1] => 28
[6,3,3,2,2] => 85
[6,3,3,2,1,1] => 41
[6,3,3,1,1,1,1] => 1
[6,3,2,2,2,1] => 94
[6,3,2,2,1,1,1] => 3
[6,3,2,1,1,1,1,1] => 0
[6,3,1,1,1,1,1,1,1] => 0
[6,2,2,2,2,2] => 50
[6,2,2,2,2,1,1] => 8
[6,2,2,2,1,1,1,1] => 0
[6,2,2,1,1,1,1,1,1] => 0
[6,2,1,1,1,1,1,1,1,1] => 0
[6,1,1,1,1,1,1,1,1,1,1] => 0
[5,5,5,1] => 64
[5,5,4,2] => 221
[5,5,4,1,1] => 120
[5,5,3,3] => 83
[5,5,3,2,1] => 188
[5,5,3,1,1,1] => 27
[5,5,2,2,2] => 92
[5,5,2,2,1,1] => 43
[5,5,2,1,1,1,1] => 1
[5,5,1,1,1,1,1,1] => 0
[5,4,4,3] => 148
[5,4,4,2,1] => 186
[5,4,4,1,1,1] => 11
[5,4,3,3,1] => 65
[5,4,3,2,2] => 127
[5,4,3,2,1,1] => 51
[5,4,3,1,1,1,1] => 0
[5,4,2,2,2,1] => 80
[5,4,2,2,1,1,1] => 3
[5,4,2,1,1,1,1,1] => 0
[5,4,1,1,1,1,1,1,1] => 0
[5,3,3,3,2] => 4
[5,3,3,3,1,1] => 4
[5,3,3,2,2,1] => 24
[5,3,3,2,1,1,1] => 2
[5,3,3,1,1,1,1,1] => 0
[5,3,2,2,2,2] => 40
[5,3,2,2,2,1,1] => 10
[5,3,2,2,1,1,1,1] => 0
[5,3,2,1,1,1,1,1,1] => 0
[5,3,1,1,1,1,1,1,1,1] => 0
[5,2,2,2,2,2,1] => 16
[5,2,2,2,2,1,1,1] => 0
[5,2,2,2,1,1,1,1,1] => 0
[5,2,2,1,1,1,1,1,1,1] => 0
[5,2,1,1,1,1,1,1,1,1,1] => 0
[5,1,1,1,1,1,1,1,1,1,1,1] => 0
[4,4,4,4] => 38
[4,4,4,3,1] => 37
[4,4,4,2,2] => 50
[4,4,4,2,1,1] => 10
[4,4,4,1,1,1,1] => 0
[4,4,3,3,2] => 10
[4,4,3,3,1,1] => 2
[4,4,3,2,2,1] => 24
[4,4,3,2,1,1,1] => 0
[4,4,3,1,1,1,1,1] => 0
[4,4,2,2,2,2] => 27
[4,4,2,2,2,1,1] => 5
[4,4,2,2,1,1,1,1] => 0
[4,4,2,1,1,1,1,1,1] => 0
[4,4,1,1,1,1,1,1,1,1] => 0
[4,3,3,3,3] => 0
[4,3,3,3,2,1] => 0
[4,3,3,3,1,1,1] => 0
[4,3,3,2,2,2] => 5
[4,3,3,2,2,1,1] => 1
[4,3,3,2,1,1,1,1] => 0
[4,3,3,1,1,1,1,1,1] => 0
[4,3,2,2,2,2,1] => 10
[4,3,2,2,2,1,1,1] => 0
[4,3,2,2,1,1,1,1,1] => 0
[4,3,2,1,1,1,1,1,1,1] => 0
[4,3,1,1,1,1,1,1,1,1,1] => 0
[4,2,2,2,2,2,2] => 11
[4,2,2,2,2,2,1,1] => 1
[4,2,2,2,2,1,1,1,1] => 0
[4,2,2,2,1,1,1,1,1,1] => 0
[4,2,2,1,1,1,1,1,1,1,1] => 0
[4,2,1,1,1,1,1,1,1,1,1,1] => 0
[4,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[3,3,3,3,3,1] => 0
[3,3,3,3,2,2] => 0
[3,3,3,3,2,1,1] => 0
[3,3,3,3,1,1,1,1] => 0
[3,3,3,2,2,2,1] => 0
[3,3,3,2,2,1,1,1] => 0
[3,3,3,2,1,1,1,1,1] => 0
[3,3,3,1,1,1,1,1,1,1] => 0
[3,3,2,2,2,2,2] => 2
[3,3,2,2,2,2,1,1] => 0
[3,3,2,2,2,1,1,1,1] => 0
[3,3,2,2,1,1,1,1,1,1] => 0
[3,3,2,1,1,1,1,1,1,1,1] => 0
[3,3,1,1,1,1,1,1,1,1,1,1] => 0
[3,2,2,2,2,2,2,1] => 2
[3,2,2,2,2,2,1,1,1] => 0
[3,2,2,2,2,1,1,1,1,1] => 0
[3,2,2,2,1,1,1,1,1,1,1] => 0
[3,2,2,1,1,1,1,1,1,1,1,1] => 0
[3,2,1,1,1,1,1,1,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[2,2,2,2,2,2,2,2] => 2
[2,2,2,2,2,2,2,1,1] => 0
[2,2,2,2,2,2,1,1,1,1] => 0
[2,2,2,2,2,1,1,1,1,1,1] => 0
[2,2,2,2,1,1,1,1,1,1,1,1] => 0
[2,2,2,1,1,1,1,1,1,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[17] => 297
[16,1] => 618
[15,2] => 1191
[15,1,1] => 415
[14,3] => 1718
[14,2,1] => 1382
[14,1,1,1] => 97
[13,4] => 2242
[13,3,1] => 2360
[13,2,2] => 1388
[13,2,1,1] => 551
[13,1,1,1,1] => 5
[12,5] => 2432
[12,4,1] => 3410
[12,3,2] => 2816
[12,3,1,1] => 1117
[12,2,2,1] => 1080
[12,2,1,1,1] => 70
[12,1,1,1,1,1] => 0
[11,6] => 2362
[11,5,1] => 3772
[11,4,2] => 4348
[11,4,1,1] => 1765
[11,3,3] => 1544
[11,3,2,1] => 2328
[11,3,1,1,1] => 196
[11,2,2,2] => 814
[11,2,2,1,1] => 286
[11,2,1,1,1,1] => 1
[11,1,1,1,1,1,1] => 0
[10,7] => 1833
[10,6,1] => 3628
[10,5,2] => 4796
[10,5,1,1] => 2007
[10,4,3] => 3329
[10,4,2,1] => 3720
[10,4,1,1,1] => 333
[10,3,3,1] => 1430
[10,3,2,2] => 1634
[10,3,2,1,1] => 688
[10,3,1,1,1,1] => 8
[10,2,2,2,1] => 479
[10,2,2,1,1,1] => 20
[10,2,1,1,1,1,1] => 0
[10,1,1,1,1,1,1,1] => 0
[9,8] => 1022
[9,7,1] => 2504
[9,6,2] => 4289
[9,6,1,1] => 1804
[9,5,3] => 3758
[9,5,2,1] => 3991
[9,5,1,1,1] => 413
[9,4,4] => 1863
[9,4,3,1] => 3148
[9,4,2,2] => 2489
[9,4,2,1,1] => 1114
[9,4,1,1,1,1] => 16
[9,3,3,2] => 1022
[9,3,3,1,1] => 483
[9,3,2,2,1] => 942
[9,3,2,1,1,1] => 70
[9,3,1,1,1,1,1] => 0
[9,2,2,2,2] => 319
[9,2,2,2,1,1] => 90
[9,2,2,1,1,1,1] => 0
[9,2,1,1,1,1,1,1] => 0
[9,1,1,1,1,1,1,1,1] => 0
[8,8,1] => 958
[8,7,2] => 2466
[8,7,1,1] => 1070
[8,6,3] => 3200
[8,6,2,1] => 3207
[8,6,1,1,1] => 315
[8,5,4] => 2308
[8,5,3,1] => 3401
[8,5,2,2] => 2431
[8,5,2,1,1] => 1172
[8,5,1,1,1,1] => 26
[8,4,4,1] => 1853
[8,4,3,2] => 2266
[8,4,3,1,1] => 1017
[8,4,2,2,1] => 1379
[8,4,2,1,1,1] => 108
[8,4,1,1,1,1,1] => 0
[8,3,3,3] => 192
[8,3,3,2,1] => 577
[8,3,3,1,1,1] => 65
[8,3,2,2,2] => 524
[8,3,2,2,1,1] => 189
[8,3,2,1,1,1,1] => 1
[8,3,1,1,1,1,1,1] => 0
[8,2,2,2,2,1] => 151
[8,2,2,2,1,1,1] => 3
[8,2,2,1,1,1,1,1] => 0
[8,2,1,1,1,1,1,1,1] => 0
[8,1,1,1,1,1,1,1,1,1] => 0
[7,7,3] => 1129
[7,7,2,1] => 1175
[7,7,1,1,1] => 143
[7,6,4] => 1697
[7,6,3,1] => 2298
[7,6,2,2] => 1555
[7,6,2,1,1] => 742
[7,6,1,1,1,1] => 13
[7,5,5] => 596
[7,5,4,1] => 2010
[7,5,3,2] => 2099
[7,5,3,1,1] => 1036
[7,5,2,2,1] => 1178
[7,5,2,1,1,1] => 121
[7,5,1,1,1,1,1] => 0
[7,4,4,2] => 1370
[7,4,4,1,1] => 576
[7,4,3,3] => 556
[7,4,3,2,1] => 1169
[7,4,3,1,1,1] => 114
[7,4,2,2,2] => 663
[7,4,2,2,1,1] => 255
[7,4,2,1,1,1,1] => 1
[7,4,1,1,1,1,1,1] => 0
[7,3,3,3,1] => 104
[7,3,3,2,2] => 236
[7,3,3,2,1,1] => 122
[7,3,3,1,1,1,1] => 2
[7,3,2,2,2,1] => 226
[7,3,2,2,1,1,1] => 11
[7,3,2,1,1,1,1,1] => 0
[7,3,1,1,1,1,1,1,1] => 0
[7,2,2,2,2,2] => 96
[7,2,2,2,2,1,1] => 20
[7,2,2,2,1,1,1,1] => 0
[7,2,2,1,1,1,1,1,1] => 0
[7,2,1,1,1,1,1,1,1,1] => 0
[7,1,1,1,1,1,1,1,1,1,1] => 0
[6,6,5] => 438
[6,6,4,1] => 963
[6,6,3,2] => 959
[6,6,3,1,1] => 403
[6,6,2,2,1] => 503
[6,6,2,1,1,1] => 38
[6,6,1,1,1,1,1] => 0
[6,5,5,1] => 427
[6,5,4,2] => 1146
[6,5,4,1,1] => 540
[6,5,3,3] => 427
[6,5,3,2,1] => 898
[6,5,3,1,1,1] => 111
[6,5,2,2,2] => 438
[6,5,2,2,1,1] => 186
[6,5,2,1,1,1,1] => 3
[6,5,1,1,1,1,1,1] => 0
[6,4,4,3] => 498
[6,4,4,2,1] => 645
[6,4,4,1,1,1] => 49
[6,4,3,3,1] => 255
[6,4,3,2,2] => 449
[6,4,3,2,1,1] => 198
[6,4,3,1,1,1,1] => 3
[6,4,2,2,2,1] => 253
[6,4,2,2,1,1,1] => 11
[6,4,2,1,1,1,1,1] => 0
[6,4,1,1,1,1,1,1,1] => 0
[6,3,3,3,2] => 24
[6,3,3,3,1,1] => 22
[6,3,3,2,2,1] => 88
[6,3,3,2,1,1,1] => 10
[6,3,3,1,1,1,1,1] => 0
[6,3,2,2,2,2] => 110
[6,3,2,2,2,1,1] => 30
[6,3,2,2,1,1,1,1] => 0
[6,3,2,1,1,1,1,1,1] => 0
[6,3,1,1,1,1,1,1,1,1] => 0
[6,2,2,2,2,2,1] => 37
[6,2,2,2,2,1,1,1] => 0
[6,2,2,2,1,1,1,1,1] => 0
[6,2,2,1,1,1,1,1,1,1] => 0
[6,2,1,1,1,1,1,1,1,1,1] => 0
[6,1,1,1,1,1,1,1,1,1,1,1] => 0
[5,5,5,2] => 109
[5,5,5,1,1] => 88
[5,5,4,3] => 215
[5,5,4,2,1] => 322
[5,5,4,1,1,1] => 50
[5,5,3,3,1] => 137
[5,5,3,2,2] => 174
[5,5,3,2,1,1] => 109
[5,5,3,1,1,1,1] => 3
[5,5,2,2,2,1] => 93
[5,5,2,2,1,1,1] => 10
[5,5,2,1,1,1,1,1] => 0
[5,5,1,1,1,1,1,1,1] => 0
[5,4,4,4] => 131
[5,4,4,3,1] => 196
[5,4,4,2,2] => 206
[5,4,4,2,1,1] => 77
[5,4,4,1,1,1,1] => 0
[5,4,3,3,2] => 68
[5,4,3,3,1,1] => 34
[5,4,3,2,2,1] => 124
[5,4,3,2,1,1,1] => 8
[5,4,3,1,1,1,1,1] => 0
[5,4,2,2,2,2] => 91
[5,4,2,2,2,1,1] => 27
[5,4,2,2,1,1,1,1] => 0
[5,4,2,1,1,1,1,1,1] => 0
[5,4,1,1,1,1,1,1,1,1] => 0
[5,3,3,3,3] => 0
[5,3,3,3,2,1] => 6
[5,3,3,3,1,1,1] => 1
[5,3,3,2,2,2] => 23
[5,3,3,2,2,1,1] => 11
[5,3,3,2,1,1,1,1] => 0
[5,3,3,1,1,1,1,1,1] => 0
[5,3,2,2,2,2,1] => 33
[5,3,2,2,2,1,1,1] => 1
[5,3,2,2,1,1,1,1,1] => 0
[5,3,2,1,1,1,1,1,1,1] => 0
[5,3,1,1,1,1,1,1,1,1,1] => 0
[5,2,2,2,2,2,2] => 23
[5,2,2,2,2,2,1,1] => 3
[5,2,2,2,2,1,1,1,1] => 0
[5,2,2,2,1,1,1,1,1,1] => 0
[5,2,2,1,1,1,1,1,1,1,1] => 0
[5,2,1,1,1,1,1,1,1,1,1,1] => 0
[5,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[4,4,4,4,1] => 46
[4,4,4,3,2] => 50
[4,4,4,3,1,1] => 10
[4,4,4,2,2,1] => 40
[4,4,4,2,1,1,1] => 0
[4,4,4,1,1,1,1,1] => 0
[4,4,3,3,3] => 0
[4,4,3,3,2,1] => 8
[4,4,3,3,1,1,1] => 0
[4,4,3,2,2,2] => 30
[4,4,3,2,2,1,1] => 6
[4,4,3,2,1,1,1,1] => 0
[4,4,3,1,1,1,1,1,1] => 0
[4,4,2,2,2,2,1] => 21
[4,4,2,2,2,1,1,1] => 0
[4,4,2,2,1,1,1,1,1] => 0
[4,4,2,1,1,1,1,1,1,1] => 0
[4,4,1,1,1,1,1,1,1,1,1] => 0
[4,3,3,3,3,1] => 0
[4,3,3,3,2,2] => 0
[4,3,3,3,2,1,1] => 0
[4,3,3,3,1,1,1,1] => 0
[4,3,3,2,2,2,1] => 4
[4,3,3,2,2,1,1,1] => 0
[4,3,3,2,1,1,1,1,1] => 0
[4,3,3,1,1,1,1,1,1,1] => 0
[4,3,2,2,2,2,2] => 14
[4,3,2,2,2,2,1,1] => 2
[4,3,2,2,2,1,1,1,1] => 0
[4,3,2,2,1,1,1,1,1,1] => 0
[4,3,2,1,1,1,1,1,1,1,1] => 0
[4,3,1,1,1,1,1,1,1,1,1,1] => 0
[4,2,2,2,2,2,2,1] => 7
[4,2,2,2,2,2,1,1,1] => 0
[4,2,2,2,2,1,1,1,1,1] => 0
[4,2,2,2,1,1,1,1,1,1,1] => 0
[4,2,2,1,1,1,1,1,1,1,1,1] => 0
[4,2,1,1,1,1,1,1,1,1,1,1,1] => 0
[4,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[3,3,3,3,3,2] => 0
[3,3,3,3,3,1,1] => 0
[3,3,3,3,2,2,1] => 0
[3,3,3,3,2,1,1,1] => 0
[3,3,3,3,1,1,1,1,1] => 0
[3,3,3,2,2,2,2] => 0
[3,3,3,2,2,2,1,1] => 0
[3,3,3,2,2,1,1,1,1] => 0
[3,3,3,2,1,1,1,1,1,1] => 0
[3,3,3,1,1,1,1,1,1,1,1] => 0
[3,3,2,2,2,2,2,1] => 1
[3,3,2,2,2,2,1,1,1] => 0
[3,3,2,2,2,1,1,1,1,1] => 0
[3,3,2,2,1,1,1,1,1,1,1] => 0
[3,3,2,1,1,1,1,1,1,1,1,1] => 0
[3,3,1,1,1,1,1,1,1,1,1,1,1] => 0
[3,2,2,2,2,2,2,2] => 4
[3,2,2,2,2,2,2,1,1] => 0
[3,2,2,2,2,2,1,1,1,1] => 0
[3,2,2,2,2,1,1,1,1,1,1] => 0
[3,2,2,2,1,1,1,1,1,1,1,1] => 0
[3,2,2,1,1,1,1,1,1,1,1,1,1] => 0
-----------------------------------------------------------------------------
Created: Sep 26, 2020 at 23:09 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Sep 26, 2020 at 23:09 by Martin Rubey