[seqfan] Re: Problem reproducing A019989, A019990, and A019991

[Sean A. Irvine]

Thanks Marc,

I now have a working Java program for these sequences (which I have added
to A019989).  The existing name/title remains very confusing, but I have no
idea what a better way to describe this would be.

Sean.


On Tue, 16 Apr 2019 at 07:29, Marc LeBrun <mlb at well.com> wrote:

> Sean, thanks but actually, Gosper just explicitly told us what he was
> doing (I'll recopy that part at the end of this reply).
> I think some of the confusion is because the OEIS description transcribes
> Macsyma's *set* union() operators as "ORs".
> (see https://people.eecs.berkeley.edu/~fateman/macsyma/docs/refman16.pdf <
> https://people.eecs.berkeley.edu/~fateman/macsyma/docs/refman16.pdf> page
> 20)
> I'm also unsure about mapping RWG's +/-1's to OEIS's floor -- I'm alas too
> hurried right now to "poofread" it properly.
> Anyway I think there's enough here now to reconstruct the correct
> algorithm...  "Enjoy"!
> [RWG's Macsyma snippet follows]:
> ========
> (c236) abc\a\b\c1(a,b,c,\a,\b,\c):=
>
> [union(3*a,3*\c+1,3*\b-1),union(3*b,3*\c-1,3*\a+1),union(3*c,3*\b+1,3*\a-1),
>
>  union(3*\a,3*c-1,3*b+1),union(3*\b,3*c+1,3*a-1),union([1],3*\c,3*a+1,3*b-1)];
>
> (d236) abcABC1(a, b, c, A, B, C) := [union(3 a, 3 C + 1, 3 B - 1),
>
> union(3 b, 3 C - 1, 3 A + 1), union(3 c, 3 B + 1, 3 A - 1),
>
> union(3 A, 3 c - 1, 3 b + 1), union(3 B, 3 c + 1, 3 a - 1),
>
> union([1], 3 C, 3 a + 1, 3 b - 1)]
>
> Initialize six empty lists:
> (c237) makelist([],k,1,6);
> (d237)                     [[], [], [], [], [], []]
>
> Then iteratively apply abcABC1,
> ...
> ========
>
> > On Apr 15, 2019, at 11:39 AM, Sean A. Irvine <sairvin at gmail.com> wrote:
> >
> > On Tue, 16 Apr 2019 at 03:30, Marc LeBrun <mlb at well.com> wrote:
> >
> >>
> >> To break the symmetry perhaps some of those operations don't commute or
> >> associate and/or maybe they are computations done sequentially, instead
> of
> >> simultaneous relations?
> >> (And, agreed, moreover there STILL needs to be a "1 --> 0" to keep
> things
> >> from saturating.)
> >>
> >
> > Some good ideas there.  I certainly had been assuming that the operations
> > were simultaneous.  Perhaps there is also some additional special
> relation
> > between a and A, b and B, c and C, otherwise why not simply label the
> later
> > functions d, e, f.
> >
> > I did also try a 3-way XOR, i.e. only true if exactly one of the
> arguments
> > true.  But so far everything I have tried results in all functions
> becoming
> > 1 or 0 eventually.
> >
> > Sean.
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
>
>
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