PacletInstall["/Users/sw/Dropbox/Physics/CodeDevelopment/Paclets/CombinatorEvolve-0.0.1.paclet"]
In[]:=
PacletObject
Name: CombinatorEvolve
Version: 0.0.1

Out[]=
<<CombinatorEvolve`
In[]:=
RepresentativeKernels[]:=Last/@First/@GatherBy[ParallelEvaluate[{$MachineName,#},#]&/@Kernels[],First]
In[]:=
SetAttributes[ParallelOnce,HoldFirst]
In[]:=
ParallelOnce[expr_]:=ParallelEvaluate[expr,RepresentativeKernels[]]
In[]:=
RepresentativeKernels[]
In[]:=
KernelObject
Name: local
KernelID: 1
,KernelObject
Name: lambda
KernelID: 26
,KernelObject
Name: tremac
KernelID: 38
,KernelObject
Name: macpro-basement
KernelID: 50
,KernelObject
Name: threadripper
KernelID: 62

Out[]=
ParallelOnce[PacletInstall["/Users/sw/Dropbox/Physics/CodeDevelopment/Paclets/CombinatorEvolve-0.0.1.paclet"]]
In[]:=
PacletInstall::readonly:The PacletManager application is running in read-only mode; paclets cannot be installed or uninstalled.
(kernel 1)
PacletInstall::readonly:The PacletManager application is running in read-only mode; paclets cannot be installed or uninstalled.
(kernel 62)
$Failed,PacletObject
Name: CombinatorEvolve
Version: 0.0.1
,PacletObject
Name: CombinatorEvolve
Version: 0.0.1
,PacletObject
Name: CombinatorEvolve
Version: 0.0.1
,$Failed
Out[]=
ParallelEvaluate[<<CombinatorEvolve`]
In[]:=
SKCombinatorLeftmostOutermostLeafCounts[s[s][s][s[s]][s][s],1000]
In[]:=
ListLinePlot[Differences[SKCombinatorLeftmostOutermostLeafCounts[s[s[s]][s][s[s[s][s]]][s],1000]],PlotRangeAll]
In[]:=
Out[]=
ListLinePlot[SKCombinatorLeftmostOutermostLeafCounts[s[s[s]][s][s[s[s][s]]][s],1000],PlotRangeAll,ScalingFunctions"Log"]
In[]:=
Out[]=
ListLinePlot[Ratios@SKCombinatorLeftmostOutermostLeafCounts[s[s[s]][s][s[s[s][s]]][s],1000],PlotRangeAll]
In[]:=
Out[]=
ListLinePlot[Ratios@SKCombinatorLeftmostOutermostLeafCounts[s[s][s[s][s]][s[s]][s][s],1000]]
In[]:=
Out[]=
ListLinePlot[Differences@SKCombinatorLeftmostOutermostLeafCounts[s[s][s[s][s]][s[s]][s][s],1000]]
In[]:=
Out[]=

SK8

A single k only

Here’s my ordering.

SK8

SK9

SK9 Selection

SK10

NOTE: assuming <4 k’s

Large array::

SK10 +