I knew about A000371. I used it in "Notes on equivalence
between boolean arrays of different rank" in the March 2015
Journal of J - right after R E Boss on Fibonacci :-)
On 2019.08.22 16:33:39, you,
the extraordinary R.E. Boss, spake thus:
> Well I think I can answer your question: there is no need to submit the
> sequence, since it already known.
> First I had to fiddle out what a (non)degenerate truth table was and was
> enlightened on this subject by Wittgenstein himself!
> Then I found out what the formula was to generate the numbers of
> non-degenerate truth tables, it appeared to be
>
> (](4 : ('+/(_1^(x-y)) * (y!x) * 2^2^y')) i.@>:)"0 >:i.8x
> 2 10 218 64594 4294642034 18446744047940725978
> 340282366920938463334247399005993378250
>
> which coincides with A000371, from which the second line reads " Number of
> nondegenerate Boolean functions of n variables."
>
> I still don't grasp what your concept of self-duality is.
>
>
> R.E. Boss
>
>
> > -----Oorspronkelijk bericht-----
> > Van: Chat <[email protected]> Namens Nollaig
> > MacKenzie
> > Verzonden: dinsdag 20 augustus 2019 06:17
> > Aan: [email protected]
> > Onderwerp: Re: [Jchat] Number of self-dual arrays of rank N; OEIS
> >
> > It is a simple slip. T is, in the NOTE:
> >
> > 0 0
> > 0 1
> >
> > 0 1
> > 1 1
> >
> > And (let us call it Tlocs):
> >
> > ]Tlocs=:Gloc L:0 (0;1)=L:0 T
> > ┌─────┬─────┐
> > │0 0 0│0 1 1│
> > │0 0 1│1 0 1│
> > │0 1 0│1 1 0│
> > │1 0 0│1 1 1│
> > └─────┴─────┘
> >
> > If you then do the |. on the second item of Tlocs:
> >
> > (0{Tlocs),|.L:0 (1{Tlocs)
> > ┌─────┬─────┐
> > │0 0 0│1 1 1│
> > │0 0 1│1 1 0│
> > │0 1 0│1 0 1│
> > │1 0 0│0 1 1│
> > └─────┴─────┘
> >
> > You have the result you want.
> >
> > (I should mention that Gloc is meant to apply to arrays of 0 and 1. I should
> > really have defined it as, perhaps, ($ #: I.@,)@:*
> >
> > Best wishes, N.
> >
> > On 2019.08.19 09:52:02, you,
> > the extraordinary R.E. Boss, spake thus:
> >
> > > I tried to understand what you wrote and am left with questions.
> > >
> > > Take
> > > [T=:(0 1 1, 1 0 1, 1 1 0,:1 1 1);0 0 0,0 0 1,0 1 0,:1 0 0
> > > +-----+-----+
> > > |0 1 1|0 0 0|
> > > |1 0 1|0 0 1|
> > > |1 1 0|0 1 0|
> > > |1 1 1|1 0 0|
> > > +-----+-----+
> > >
> > > With Gloc=: $ #: I.@, from the Journal of J, I get
> > > Gloc L:0 (0;1)=L:0 T
> > > +---+---+
> > > |0 0|1 2|
> > > |1 1|2 1|
> > > |2 2|3 0|
> > > +---+---+
> > > From this I get
> > > (, (>:@$|"1 -.)L:0,:~-.L:0)Gloc L:0 (0;1)=L:0 T
> > > +-----+-----+
> > > |0 0 |1 2 |
> > > |1 1 |2 1 |
> > > |2 2 |3 0 |
> > > +-----+-----+
> > > | 1 1| 0 _1|
> > > | 0 0|_1 0|
> > > |_1 _1|_2 1|
> > > +-----+-----+
> > > |1 1 |0 2 |
> > > |0 0 |3 0 |
> > > |3 2 |2 1 |
> > > +-----+-----+
> > > Which are the original locations of 0 and 1 respectively, there negations
> > > (-.),
> > and these converted to locations.
> > > Being selfdual we should have the first and the reversed latest row to be
> > equal, however
> > > (-: [:|. (>:@$|"1 -.)L:0)Gloc L:0 (0;1)=L:0 T
> > > 0
> > >
> > > What do I do wrong?
> > >
> > >
> > > R.E. Boss
> > ----------------------------------------------------------------------
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> ----------------------------------------------------------------------
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