[seqfan] Re: Interesting sequence needs one more term (lattices of subsets)

[Neil Sloane]

1,1,1,4,50,7443, which makes it different from
all the other 1,4,50's - nice work!

Will you update the entry (A235604), and tell Donald Davis about your work?

Best regards
Neil




On Mon, Jan 27, 2014 at 10:56 PM, Andrew Weimholt <andrew.weimholt at gmail.com
> wrote:

> Hi Neil,
>
> I've computed the number of realizable equivalence classes for n=5, and got
> 7443.
> My program also confirmed 50 for n=4.
>
> Instead of constructing the equivalence classes first, I construct the
> realizations
> then compute the equivalence class, test to see if it is canonical, and if
> so,
> I make sure I haven't already counted it, and if it's new, I increment my
> count.
>
> There are 2^n ways in which an element can belong to n labeled sets.
> We can throw out the element that belongs to no sets, and the one that
> belongs
> to all n sets, as those two elements do not help us distinguish one
> collection of
> sets from another. This leaves us with 2^n-2 elements to play with, and
> every subset of these 2^n-2 elements forms a realization of some
> equivalence
> class. This gives me 2^(2^n-2) realizations to examine (2^30 for n=5).
>
> Next I'll write a program which constructs the equivalence classes first,
> without caring if they're realizable. I suspect that all equivalence
> classes
> with non-contradictory inclusion relations will be realizable, and the
> number should
> come out the same.
>
> Andrew
>
>
>
> On Tue, Jan 21, 2014 at 7:32 PM, Neil Sloane <njasloane at gmail.com> wrote:
>
> > Dear Seq Fans, http://oeis.org/A235604 looks very interesting,
> > so I created an entry for it even though there
> > are already many sequences that start the same way
> > (1,4,50). If we had one more term, it might settle
> > the question of whether it is really new. My guess is that it will be
> new.
> > Neil
> >
> > --
> > Dear Friends, I have now retired from AT&T. New coordinates:
> >
> > Neil J. A. Sloane, President, OEIS Foundation
> > 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> > Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> > Phone: 732 828 6098; home page: http://NeilSloane.com
> > Email: njasloane at gmail.com
> >
> > _______________________________________________
> >
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> >
>
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>
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>



-- 
Dear Friends, I have now retired from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com