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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, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
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-----------------------------------------------------------------------------
Statistic identifier: St001283
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The number of finite solvable groups that are realised by the given partition over the complex numbers.
A finite group $G$ is ''realised'' by the partition $(a_1,\dots,a_m)$ if its group algebra over the complex numbers is isomorphic to the direct product of $a_i\times a_i$ matrix rings over the complex numbers.
The smallest partition which does not realise a solvable group, but does realise a finite group, is $(5,4,3,3,1)$.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
@cached_function
def small_solvable_group_degrees(n):
return [(G, Partition(sorted([ZZ(e) for e,f in G.CharacterDegrees() for i in range(ZZ(f))], reverse=True)))
for G in gap.AllSmallGroups(n) if G.IsSolvableGroup().sage()]
def statistic(la):
n = sum(e^2 for e in la)
return sum(1 for G, mu in small_solvable_group_degrees(n) if mu == la)
-----------------------------------------------------------------------------
Statistic values:
[1] => 1
[2] => 0
[1,1] => 1
[3] => 0
[2,1] => 0
[1,1,1] => 1
[4] => 0
[3,1] => 0
[2,2] => 0
[2,1,1] => 1
[1,1,1,1] => 2
[5] => 0
[4,1] => 0
[3,2] => 0
[3,1,1] => 0
[2,2,1] => 0
[2,1,1,1] => 0
[1,1,1,1,1] => 1
[6] => 0
[5,1] => 0
[4,2] => 0
[4,1,1] => 0
[3,3] => 0
[3,2,1] => 0
[3,1,1,1] => 1
[2,2,2] => 0
[2,2,1,1] => 1
[2,1,1,1,1] => 2
[1,1,1,1,1,1] => 1
[7] => 0
[6,1] => 0
[5,2] => 0
[5,1,1] => 0
[4,3] => 0
[4,2,1] => 0
[4,1,1,1] => 0
[3,3,1] => 0
[3,2,2] => 0
[3,2,1,1] => 0
[3,1,1,1,1] => 0
[2,2,2,1] => 0
[2,2,1,1,1] => 0
[2,1,1,1,1,1] => 0
[1,1,1,1,1,1,1] => 1
[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] => 1
[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] => 1
[2,2,1,1,1,1] => 2
[2,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1] => 3
[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] => 1
[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] => 2
[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] => 1
[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] => 2
[2,2,2,1,1,1,1] => 3
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[3,2,2,2,2,1] => 0
[3,2,2,2,1,1,1] => 1
[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] => 1
[2,2,2,2,1,1,1,1] => 2
[2,2,2,1,1,1,1,1,1] => 1
[2,2,1,1,1,1,1,1,1,1] => 6
[2,1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1,1,1] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[2,2,2,2,2,1,1,1,1] => 3
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[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] => 1
[4,2,2,2,1,1,1,1,1,1] => 0
[4,2,2,1,1,1,1,1,1,1,1] => 5
[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] => 1
[2,2,2,2,2,2,1,1,1,1] => 2
[2,2,2,2,2,1,1,1,1,1,1] => 0
[2,2,2,2,1,1,1,1,1,1,1,1] => 4
[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] => 5
[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
-----------------------------------------------------------------------------
Created: Nov 04, 2018 at 00:57 by Rene Marczinzik
-----------------------------------------------------------------------------
Last Updated: Nov 04, 2018 at 20:33 by Martin Rubey