*****************************************************************************
* 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: St001600
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple graphs.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(mu):
s = SymmetricFunctions(QQ).s()
F = species.SimpleGraphSpecies().cycle_index_series()
return F.coefficient(mu.size()).scalar(s(mu))
-----------------------------------------------------------------------------
Statistic values:
[1] => 1
[2] => 2
[1,1] => 0
[3] => 4
[2,1] => 2
[1,1,1] => 0
[4] => 11
[3,1] => 9
[2,2] => 8
[2,1,1] => 3
[1,1,1,1] => 1
[5] => 34
[4,1] => 56
[3,2] => 58
[3,1,1] => 36
[2,2,1] => 38
[2,1,1,1] => 16
[1,1,1,1,1] => 6
[6] => 156
[5,1] => 388
[4,2] => 600
[4,1,1] => 460
[3,3] => 264
[3,2,1] => 712
[3,1,1,1] => 340
[2,2,2] => 240
[2,2,1,1] => 288
[2,1,1,1,1] => 148
[1,1,1,1,1,1] => 28
[7] => 1044
[6,1] => 4052
[5,2] => 8032
[5,1,1] => 7236
[4,3] => 7236
[4,2,1] => 15788
[4,1,1,1] => 7720
[3,3,1] => 8844
[3,2,2] => 8788
[3,2,1,1] => 12948
[3,1,1,1,1] => 5036
[2,2,2,1] => 5052
[2,2,1,1,1] => 4416
[2,1,1,1,1,1] => 1788
[1,1,1,1,1,1,1] => 252
[8] => 0
[7,1] => 0
[6,2] => 0
[6,1,1] => 0
[5,3] => 0
[5,2,1] => 0
[5,1,1,1] => 0
[4,4] => 0
[4,3,1] => 0
[4,2,2] => 0
[4,2,1,1] => 0
[4,1,1,1,1] => 0
[3,3,2] => 0
[3,3,1,1] => 0
[3,2,2,1] => 0
[3,2,1,1,1] => 0
[3,1,1,1,1,1] => 0
[2,2,2,2] => 0
[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] => 0
[8,1] => 0
[7,2] => 0
[7,1,1] => 0
[6,3] => 0
[6,2,1] => 0
[6,1,1,1] => 0
[5,4] => 0
[5,3,1] => 0
[5,2,2] => 0
[5,2,1,1] => 0
[5,1,1,1,1] => 0
[4,4,1] => 0
[4,3,2] => 0
[4,3,1,1] => 0
[4,2,2,1] => 0
[4,2,1,1,1] => 0
[4,1,1,1,1,1] => 0
[3,3,3] => 0
[3,3,2,1] => 0
[3,3,1,1,1] => 0
[3,2,2,2] => 0
[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] => 0
[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] => 0
[9,1] => 0
[8,2] => 0
[8,1,1] => 0
[7,3] => 0
[7,2,1] => 0
[7,1,1,1] => 0
[6,4] => 0
[6,3,1] => 0
[6,2,2] => 0
[6,2,1,1] => 0
[6,1,1,1,1] => 0
[5,5] => 0
[5,4,1] => 0
[5,3,2] => 0
[5,3,1,1] => 0
[5,2,2,1] => 0
[5,2,1,1,1] => 0
[5,1,1,1,1,1] => 0
[4,4,2] => 0
[4,4,1,1] => 0
[4,3,3] => 0
[4,3,2,1] => 0
[4,3,1,1,1] => 0
[4,2,2,2] => 0
[4,2,2,1,1] => 0
[4,2,1,1,1,1] => 0
[4,1,1,1,1,1,1] => 0
[3,3,3,1] => 0
[3,3,2,2] => 0
[3,3,2,1,1] => 0
[3,3,1,1,1,1] => 0
[3,2,2,2,1] => 0
[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] => 0
[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] => 0
[10,1] => 0
[9,2] => 0
[9,1,1] => 0
[8,3] => 0
[8,2,1] => 0
[8,1,1,1] => 0
[7,4] => 0
[7,3,1] => 0
[7,2,2] => 0
[7,2,1,1] => 0
[7,1,1,1,1] => 0
[6,5] => 0
[6,4,1] => 0
[6,3,2] => 0
[6,3,1,1] => 0
[6,2,2,1] => 0
[6,2,1,1,1] => 0
[6,1,1,1,1,1] => 0
[5,5,1] => 0
[5,4,2] => 0
[5,4,1,1] => 0
[5,3,3] => 0
[5,3,2,1] => 0
[5,3,1,1,1] => 0
[5,2,2,2] => 0
[5,2,2,1,1] => 0
[5,2,1,1,1,1] => 0
[5,1,1,1,1,1,1] => 0
[4,4,3] => 0
[4,4,2,1] => 0
[4,4,1,1,1] => 0
[4,3,3,1] => 0
[4,3,2,2] => 0
[4,3,2,1,1] => 0
[4,3,1,1,1,1] => 0
[4,2,2,2,1] => 0
[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] => 0
[3,3,2,1,1,1] => 0
[3,3,1,1,1,1,1] => 0
[3,2,2,2,2] => 0
[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] => 0
[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] => 0
[11,1] => 0
[10,2] => 0
[10,1,1] => 0
[9,3] => 0
[9,2,1] => 0
[9,1,1,1] => 0
[8,4] => 0
[8,3,1] => 0
[8,2,2] => 0
[8,2,1,1] => 0
[8,1,1,1,1] => 0
[7,5] => 0
[7,4,1] => 0
[7,3,2] => 0
[7,3,1,1] => 0
[7,2,2,1] => 0
[7,2,1,1,1] => 0
[7,1,1,1,1,1] => 0
[6,6] => 0
[6,5,1] => 0
[6,4,2] => 0
[6,4,1,1] => 0
[6,3,3] => 0
[6,3,2,1] => 0
[6,3,1,1,1] => 0
[6,2,2,2] => 0
[6,2,2,1,1] => 0
[6,2,1,1,1,1] => 0
[6,1,1,1,1,1,1] => 0
[5,5,2] => 0
[5,5,1,1] => 0
[5,4,3] => 0
[5,4,2,1] => 0
[5,4,1,1,1] => 0
[5,3,3,1] => 0
[5,3,2,2] => 0
[5,3,2,1,1] => 0
[5,3,1,1,1,1] => 0
[5,2,2,2,1] => 0
[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] => 0
[4,4,3,1] => 0
[4,4,2,2] => 0
[4,4,2,1,1] => 0
[4,4,1,1,1,1] => 0
[4,3,3,2] => 0
[4,3,3,1,1] => 0
[4,3,2,2,1] => 0
[4,3,2,1,1,1] => 0
[4,3,1,1,1,1,1] => 0
[4,2,2,2,2] => 0
[4,2,2,2,1,1] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[12,1] => 0
[11,2] => 0
[11,1,1] => 0
[10,3] => 0
[10,2,1] => 0
[10,1,1,1] => 0
[9,4] => 0
[9,3,1] => 0
[9,2,2] => 0
[9,2,1,1] => 0
[9,1,1,1,1] => 0
[8,5] => 0
[8,4,1] => 0
[8,3,2] => 0
[8,3,1,1] => 0
[8,2,2,1] => 0
[8,2,1,1,1] => 0
[8,1,1,1,1,1] => 0
[7,6] => 0
[7,5,1] => 0
[7,4,2] => 0
[7,4,1,1] => 0
[7,3,3] => 0
[7,3,2,1] => 0
[7,3,1,1,1] => 0
[7,2,2,2] => 0
[7,2,2,1,1] => 0
[7,2,1,1,1,1] => 0
[7,1,1,1,1,1,1] => 0
[6,6,1] => 0
[6,5,2] => 0
[6,5,1,1] => 0
[6,4,3] => 0
[6,4,2,1] => 0
[6,4,1,1,1] => 0
[6,3,3,1] => 0
[6,3,2,2] => 0
[6,3,2,1,1] => 0
[6,3,1,1,1,1] => 0
[6,2,2,2,1] => 0
[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] => 0
[5,5,2,1] => 0
[5,5,1,1,1] => 0
[5,4,4] => 0
[5,4,3,1] => 0
[5,4,2,2] => 0
[5,4,2,1,1] => 0
[5,4,1,1,1,1] => 0
[5,3,3,2] => 0
[5,3,3,1,1] => 0
[5,3,2,2,1] => 0
[5,3,2,1,1,1] => 0
[5,3,1,1,1,1,1] => 0
[5,2,2,2,2] => 0
[5,2,2,2,1,1] => 0
[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] => 0
[4,4,3,2] => 0
[4,4,3,1,1] => 0
[4,4,2,2,1] => 0
[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] => 0
[4,3,3,1,1,1] => 0
[4,3,2,2,2] => 0
[4,3,2,2,1,1] => 0
[4,3,2,1,1,1,1] => 0
[4,3,1,1,1,1,1,1] => 0
[4,2,2,2,2,1] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[13,1] => 0
[12,2] => 0
[12,1,1] => 0
[11,3] => 0
[11,2,1] => 0
[11,1,1,1] => 0
[10,4] => 0
[10,3,1] => 0
[10,2,2] => 0
[10,2,1,1] => 0
[10,1,1,1,1] => 0
[9,5] => 0
[9,4,1] => 0
[9,3,2] => 0
[9,3,1,1] => 0
[9,2,2,1] => 0
[9,2,1,1,1] => 0
[9,1,1,1,1,1] => 0
[8,6] => 0
[8,5,1] => 0
[8,4,2] => 0
[8,4,1,1] => 0
[8,3,3] => 0
[8,3,2,1] => 0
[8,3,1,1,1] => 0
[8,2,2,2] => 0
[8,2,2,1,1] => 0
[8,2,1,1,1,1] => 0
[8,1,1,1,1,1,1] => 0
[7,7] => 0
[7,6,1] => 0
[7,5,2] => 0
[7,5,1,1] => 0
[7,4,3] => 0
[7,4,2,1] => 0
[7,4,1,1,1] => 0
[7,3,3,1] => 0
[7,3,2,2] => 0
[7,3,2,1,1] => 0
[7,3,1,1,1,1] => 0
[7,2,2,2,1] => 0
[7,2,2,1,1,1] => 0
[7,2,1,1,1,1,1] => 0
[7,1,1,1,1,1,1,1] => 0
[6,6,2] => 0
[6,6,1,1] => 0
[6,5,3] => 0
[6,5,2,1] => 0
[6,5,1,1,1] => 0
[6,4,4] => 0
[6,4,3,1] => 0
[6,4,2,2] => 0
[6,4,2,1,1] => 0
[6,4,1,1,1,1] => 0
[6,3,3,2] => 0
[6,3,3,1,1] => 0
[6,3,2,2,1] => 0
[6,3,2,1,1,1] => 0
[6,3,1,1,1,1,1] => 0
[6,2,2,2,2] => 0
[6,2,2,2,1,1] => 0
[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] => 0
[5,5,3,1] => 0
[5,5,2,2] => 0
[5,5,2,1,1] => 0
[5,5,1,1,1,1] => 0
[5,4,4,1] => 0
[5,4,3,2] => 0
[5,4,3,1,1] => 0
[5,4,2,2,1] => 0
[5,4,2,1,1,1] => 0
[5,4,1,1,1,1,1] => 0
[5,3,3,3] => 0
[5,3,3,2,1] => 0
[5,3,3,1,1,1] => 0
[5,3,2,2,2] => 0
[5,3,2,2,1,1] => 0
[5,3,2,1,1,1,1] => 0
[5,3,1,1,1,1,1,1] => 0
[5,2,2,2,2,1] => 0
[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] => 0
[4,4,4,1,1] => 0
[4,4,3,3] => 0
[4,4,3,2,1] => 0
[4,4,3,1,1,1] => 0
[4,4,2,2,2] => 0
[4,4,2,2,1,1] => 0
[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] => 0
[4,3,3,2,1,1] => 0
[4,3,3,1,1,1,1] => 0
[4,3,2,2,2,1] => 0
[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] => 0
[4,2,2,2,2,1,1] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[14,1] => 0
[13,2] => 0
[13,1,1] => 0
[12,3] => 0
[12,2,1] => 0
[12,1,1,1] => 0
[11,4] => 0
[11,3,1] => 0
[11,2,2] => 0
[11,2,1,1] => 0
[11,1,1,1,1] => 0
[10,5] => 0
[10,4,1] => 0
[10,3,2] => 0
[10,3,1,1] => 0
[10,2,2,1] => 0
[10,2,1,1,1] => 0
[10,1,1,1,1,1] => 0
[9,6] => 0
[9,5,1] => 0
[9,4,2] => 0
[9,4,1,1] => 0
[9,3,3] => 0
[9,3,2,1] => 0
[9,3,1,1,1] => 0
[9,2,2,2] => 0
[9,2,2,1,1] => 0
[9,2,1,1,1,1] => 0
[9,1,1,1,1,1,1] => 0
[8,7] => 0
[8,6,1] => 0
[8,5,2] => 0
[8,5,1,1] => 0
[8,4,3] => 0
[8,4,2,1] => 0
[8,4,1,1,1] => 0
[8,3,3,1] => 0
[8,3,2,2] => 0
[8,3,2,1,1] => 0
[8,3,1,1,1,1] => 0
[8,2,2,2,1] => 0
[8,2,2,1,1,1] => 0
[8,2,1,1,1,1,1] => 0
[8,1,1,1,1,1,1,1] => 0
[7,7,1] => 0
[7,6,2] => 0
[7,6,1,1] => 0
[7,5,3] => 0
[7,5,2,1] => 0
[7,5,1,1,1] => 0
[7,4,4] => 0
[7,4,3,1] => 0
[7,4,2,2] => 0
[7,4,2,1,1] => 0
[7,4,1,1,1,1] => 0
[7,3,3,2] => 0
[7,3,3,1,1] => 0
[7,3,2,2,1] => 0
[7,3,2,1,1,1] => 0
[7,3,1,1,1,1,1] => 0
[7,2,2,2,2] => 0
[7,2,2,2,1,1] => 0
[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] => 0
[6,6,2,1] => 0
[6,6,1,1,1] => 0
[6,5,4] => 0
[6,5,3,1] => 0
[6,5,2,2] => 0
[6,5,2,1,1] => 0
[6,5,1,1,1,1] => 0
[6,4,4,1] => 0
[6,4,3,2] => 0
[6,4,3,1,1] => 0
[6,4,2,2,1] => 0
[6,4,2,1,1,1] => 0
[6,4,1,1,1,1,1] => 0
[6,3,3,3] => 0
[6,3,3,2,1] => 0
[6,3,3,1,1,1] => 0
[6,3,2,2,2] => 0
[6,3,2,2,1,1] => 0
[6,3,2,1,1,1,1] => 0
[6,3,1,1,1,1,1,1] => 0
[6,2,2,2,2,1] => 0
[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] => 0
[5,5,4,1] => 0
[5,5,3,2] => 0
[5,5,3,1,1] => 0
[5,5,2,2,1] => 0
[5,5,2,1,1,1] => 0
[5,5,1,1,1,1,1] => 0
[5,4,4,2] => 0
[5,4,4,1,1] => 0
[5,4,3,3] => 0
[5,4,3,2,1] => 0
[5,4,3,1,1,1] => 0
[5,4,2,2,2] => 0
[5,4,2,2,1,1] => 0
[5,4,2,1,1,1,1] => 0
[5,4,1,1,1,1,1,1] => 0
[5,3,3,3,1] => 0
[5,3,3,2,2] => 0
[5,3,3,2,1,1] => 0
[5,3,3,1,1,1,1] => 0
[5,3,2,2,2,1] => 0
[5,3,2,2,1,1,1] => 0
[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] => 0
[5,2,2,2,2,1,1] => 0
[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] => 0
[4,4,4,2,1] => 0
[4,4,4,1,1,1] => 0
[4,4,3,3,1] => 0
[4,4,3,2,2] => 0
[4,4,3,2,1,1] => 0
[4,4,3,1,1,1,1] => 0
[4,4,2,2,2,1] => 0
[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] => 0
[4,3,3,2,1,1,1] => 0
[4,3,3,1,1,1,1,1] => 0
[4,3,2,2,2,2] => 0
[4,3,2,2,2,1,1] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[15,1] => 0
[14,2] => 0
[14,1,1] => 0
[13,3] => 0
[13,2,1] => 0
[13,1,1,1] => 0
[12,4] => 0
[12,3,1] => 0
[12,2,2] => 0
[12,2,1,1] => 0
[12,1,1,1,1] => 0
[11,5] => 0
[11,4,1] => 0
[11,3,2] => 0
[11,3,1,1] => 0
[11,2,2,1] => 0
[11,2,1,1,1] => 0
[11,1,1,1,1,1] => 0
[10,6] => 0
[10,5,1] => 0
[10,4,2] => 0
[10,4,1,1] => 0
[10,3,3] => 0
[10,3,2,1] => 0
[10,3,1,1,1] => 0
[10,2,2,2] => 0
[10,2,2,1,1] => 0
[10,2,1,1,1,1] => 0
[10,1,1,1,1,1,1] => 0
[9,7] => 0
[9,6,1] => 0
[9,5,2] => 0
[9,5,1,1] => 0
[9,4,3] => 0
[9,4,2,1] => 0
[9,4,1,1,1] => 0
[9,3,3,1] => 0
[9,3,2,2] => 0
[9,3,2,1,1] => 0
[9,3,1,1,1,1] => 0
[9,2,2,2,1] => 0
[9,2,2,1,1,1] => 0
[9,2,1,1,1,1,1] => 0
[9,1,1,1,1,1,1,1] => 0
[8,8] => 0
[8,7,1] => 0
[8,6,2] => 0
[8,6,1,1] => 0
[8,5,3] => 0
[8,5,2,1] => 0
[8,5,1,1,1] => 0
[8,4,4] => 0
[8,4,3,1] => 0
[8,4,2,2] => 0
[8,4,2,1,1] => 0
[8,4,1,1,1,1] => 0
[8,3,3,2] => 0
[8,3,3,1,1] => 0
[8,3,2,2,1] => 0
[8,3,2,1,1,1] => 0
[8,3,1,1,1,1,1] => 0
[8,2,2,2,2] => 0
[8,2,2,2,1,1] => 0
[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] => 0
[7,7,1,1] => 0
[7,6,3] => 0
[7,6,2,1] => 0
[7,6,1,1,1] => 0
[7,5,4] => 0
[7,5,3,1] => 0
[7,5,2,2] => 0
[7,5,2,1,1] => 0
[7,5,1,1,1,1] => 0
[7,4,4,1] => 0
[7,4,3,2] => 0
[7,4,3,1,1] => 0
[7,4,2,2,1] => 0
[7,4,2,1,1,1] => 0
[7,4,1,1,1,1,1] => 0
[7,3,3,3] => 0
[7,3,3,2,1] => 0
[7,3,3,1,1,1] => 0
[7,3,2,2,2] => 0
[7,3,2,2,1,1] => 0
[7,3,2,1,1,1,1] => 0
[7,3,1,1,1,1,1,1] => 0
[7,2,2,2,2,1] => 0
[7,2,2,2,1,1,1] => 0
[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] => 0
[6,6,3,1] => 0
[6,6,2,2] => 0
[6,6,2,1,1] => 0
[6,6,1,1,1,1] => 0
[6,5,5] => 0
[6,5,4,1] => 0
[6,5,3,2] => 0
[6,5,3,1,1] => 0
[6,5,2,2,1] => 0
[6,5,2,1,1,1] => 0
[6,5,1,1,1,1,1] => 0
[6,4,4,2] => 0
[6,4,4,1,1] => 0
[6,4,3,3] => 0
[6,4,3,2,1] => 0
[6,4,3,1,1,1] => 0
[6,4,2,2,2] => 0
[6,4,2,2,1,1] => 0
[6,4,2,1,1,1,1] => 0
[6,4,1,1,1,1,1,1] => 0
[6,3,3,3,1] => 0
[6,3,3,2,2] => 0
[6,3,3,2,1,1] => 0
[6,3,3,1,1,1,1] => 0
[6,3,2,2,2,1] => 0
[6,3,2,2,1,1,1] => 0
[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] => 0
[6,2,2,2,2,1,1] => 0
[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] => 0
[5,5,4,2] => 0
[5,5,4,1,1] => 0
[5,5,3,3] => 0
[5,5,3,2,1] => 0
[5,5,3,1,1,1] => 0
[5,5,2,2,2] => 0
[5,5,2,2,1,1] => 0
[5,5,2,1,1,1,1] => 0
[5,5,1,1,1,1,1,1] => 0
[5,4,4,3] => 0
[5,4,4,2,1] => 0
[5,4,4,1,1,1] => 0
[5,4,3,3,1] => 0
[5,4,3,2,2] => 0
[5,4,3,2,1,1] => 0
[5,4,3,1,1,1,1] => 0
[5,4,2,2,2,1] => 0
[5,4,2,2,1,1,1] => 0
[5,4,2,1,1,1,1,1] => 0
[5,4,1,1,1,1,1,1,1] => 0
[5,3,3,3,2] => 0
[5,3,3,3,1,1] => 0
[5,3,3,2,2,1] => 0
[5,3,3,2,1,1,1] => 0
[5,3,3,1,1,1,1,1] => 0
[5,3,2,2,2,2] => 0
[5,3,2,2,2,1,1] => 0
[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] => 0
[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] => 0
[4,4,4,3,1] => 0
[4,4,4,2,2] => 0
[4,4,4,2,1,1] => 0
[4,4,4,1,1,1,1] => 0
[4,4,3,3,2] => 0
[4,4,3,3,1,1] => 0
[4,4,3,2,2,1] => 0
[4,4,3,2,1,1,1] => 0
[4,4,3,1,1,1,1,1] => 0
[4,4,2,2,2,2] => 0
[4,4,2,2,2,1,1] => 0
[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] => 0
[4,3,3,2,2,1,1] => 0
[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] => 0
[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] => 0
[4,2,2,2,2,2,1,1] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[16,1] => 0
[15,2] => 0
[15,1,1] => 0
[14,3] => 0
[14,2,1] => 0
[14,1,1,1] => 0
[13,4] => 0
[13,3,1] => 0
[13,2,2] => 0
[13,2,1,1] => 0
[13,1,1,1,1] => 0
[12,5] => 0
[12,4,1] => 0
[12,3,2] => 0
[12,3,1,1] => 0
[12,2,2,1] => 0
[12,2,1,1,1] => 0
[12,1,1,1,1,1] => 0
[11,6] => 0
[11,5,1] => 0
[11,4,2] => 0
[11,4,1,1] => 0
[11,3,3] => 0
[11,3,2,1] => 0
[11,3,1,1,1] => 0
[11,2,2,2] => 0
[11,2,2,1,1] => 0
[11,2,1,1,1,1] => 0
[11,1,1,1,1,1,1] => 0
[10,7] => 0
[10,6,1] => 0
[10,5,2] => 0
[10,5,1,1] => 0
[10,4,3] => 0
[10,4,2,1] => 0
[10,4,1,1,1] => 0
[10,3,3,1] => 0
[10,3,2,2] => 0
[10,3,2,1,1] => 0
[10,3,1,1,1,1] => 0
[10,2,2,2,1] => 0
[10,2,2,1,1,1] => 0
[10,2,1,1,1,1,1] => 0
[10,1,1,1,1,1,1,1] => 0
[9,8] => 0
[9,7,1] => 0
[9,6,2] => 0
[9,6,1,1] => 0
[9,5,3] => 0
[9,5,2,1] => 0
[9,5,1,1,1] => 0
[9,4,4] => 0
[9,4,3,1] => 0
[9,4,2,2] => 0
[9,4,2,1,1] => 0
[9,4,1,1,1,1] => 0
[9,3,3,2] => 0
[9,3,3,1,1] => 0
[9,3,2,2,1] => 0
[9,3,2,1,1,1] => 0
[9,3,1,1,1,1,1] => 0
[9,2,2,2,2] => 0
[9,2,2,2,1,1] => 0
[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] => 0
[8,7,2] => 0
[8,7,1,1] => 0
[8,6,3] => 0
[8,6,2,1] => 0
[8,6,1,1,1] => 0
[8,5,4] => 0
[8,5,3,1] => 0
[8,5,2,2] => 0
[8,5,2,1,1] => 0
[8,5,1,1,1,1] => 0
[8,4,4,1] => 0
[8,4,3,2] => 0
[8,4,3,1,1] => 0
[8,4,2,2,1] => 0
[8,4,2,1,1,1] => 0
[8,4,1,1,1,1,1] => 0
[8,3,3,3] => 0
[8,3,3,2,1] => 0
[8,3,3,1,1,1] => 0
[8,3,2,2,2] => 0
[8,3,2,2,1,1] => 0
[8,3,2,1,1,1,1] => 0
[8,3,1,1,1,1,1,1] => 0
[8,2,2,2,2,1] => 0
[8,2,2,2,1,1,1] => 0
[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] => 0
[7,7,2,1] => 0
[7,7,1,1,1] => 0
[7,6,4] => 0
[7,6,3,1] => 0
[7,6,2,2] => 0
[7,6,2,1,1] => 0
[7,6,1,1,1,1] => 0
[7,5,5] => 0
[7,5,4,1] => 0
[7,5,3,2] => 0
[7,5,3,1,1] => 0
[7,5,2,2,1] => 0
[7,5,2,1,1,1] => 0
[7,5,1,1,1,1,1] => 0
[7,4,4,2] => 0
[7,4,4,1,1] => 0
[7,4,3,3] => 0
[7,4,3,2,1] => 0
[7,4,3,1,1,1] => 0
[7,4,2,2,2] => 0
[7,4,2,2,1,1] => 0
[7,4,2,1,1,1,1] => 0
[7,4,1,1,1,1,1,1] => 0
[7,3,3,3,1] => 0
[7,3,3,2,2] => 0
[7,3,3,2,1,1] => 0
[7,3,3,1,1,1,1] => 0
[7,3,2,2,2,1] => 0
[7,3,2,2,1,1,1] => 0
[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] => 0
[7,2,2,2,2,1,1] => 0
[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] => 0
[6,6,4,1] => 0
[6,6,3,2] => 0
[6,6,3,1,1] => 0
[6,6,2,2,1] => 0
[6,6,2,1,1,1] => 0
[6,6,1,1,1,1,1] => 0
[6,5,5,1] => 0
[6,5,4,2] => 0
[6,5,4,1,1] => 0
[6,5,3,3] => 0
[6,5,3,2,1] => 0
[6,5,3,1,1,1] => 0
[6,5,2,2,2] => 0
[6,5,2,2,1,1] => 0
[6,5,2,1,1,1,1] => 0
[6,5,1,1,1,1,1,1] => 0
[6,4,4,3] => 0
[6,4,4,2,1] => 0
[6,4,4,1,1,1] => 0
[6,4,3,3,1] => 0
[6,4,3,2,2] => 0
[6,4,3,2,1,1] => 0
[6,4,3,1,1,1,1] => 0
[6,4,2,2,2,1] => 0
[6,4,2,2,1,1,1] => 0
[6,4,2,1,1,1,1,1] => 0
[6,4,1,1,1,1,1,1,1] => 0
[6,3,3,3,2] => 0
[6,3,3,3,1,1] => 0
[6,3,3,2,2,1] => 0
[6,3,3,2,1,1,1] => 0
[6,3,3,1,1,1,1,1] => 0
[6,3,2,2,2,2] => 0
[6,3,2,2,2,1,1] => 0
[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] => 0
[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] => 0
[5,5,5,1,1] => 0
[5,5,4,3] => 0
[5,5,4,2,1] => 0
[5,5,4,1,1,1] => 0
[5,5,3,3,1] => 0
[5,5,3,2,2] => 0
[5,5,3,2,1,1] => 0
[5,5,3,1,1,1,1] => 0
[5,5,2,2,2,1] => 0
[5,5,2,2,1,1,1] => 0
[5,5,2,1,1,1,1,1] => 0
[5,5,1,1,1,1,1,1,1] => 0
[5,4,4,4] => 0
[5,4,4,3,1] => 0
[5,4,4,2,2] => 0
[5,4,4,2,1,1] => 0
[5,4,4,1,1,1,1] => 0
[5,4,3,3,2] => 0
[5,4,3,3,1,1] => 0
[5,4,3,2,2,1] => 0
[5,4,3,2,1,1,1] => 0
[5,4,3,1,1,1,1,1] => 0
[5,4,2,2,2,2] => 0
[5,4,2,2,2,1,1] => 0
[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] => 0
[5,3,3,3,1,1,1] => 0
[5,3,3,2,2,2] => 0
[5,3,3,2,2,1,1] => 0
[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] => 0
[5,3,2,2,2,1,1,1] => 0
[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] => 0
[5,2,2,2,2,2,1,1] => 0
[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] => 0
[4,4,4,3,2] => 0
[4,4,4,3,1,1] => 0
[4,4,4,2,2,1] => 0
[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] => 0
[4,4,3,3,1,1,1] => 0
[4,4,3,2,2,2] => 0
[4,4,3,2,2,1,1] => 0
[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] => 0
[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] => 0
[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] => 0
[4,3,2,2,2,2,1,1] => 0
[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] => 0
[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] => 0
[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] => 0
[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 23:20 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Sep 26, 2020 at 23:20 by Martin Rubey