[seqfan] Re: What is THE random permutation?

[Neil Sloane]

Allan, Thank you very much for looking into that business!
Pity the answer is "no sequence here".  I guess it
was too much to hope for that the permutation to end
all permutations had managed to stay out of the OEIS
for all these years...

Best regards
Neil

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


On Thu, Jun 25, 2015 at 1:48 PM, Allan Wechsler <acwacw at gmail.com> wrote:

> I nosed into the paper far enough to understand that the so-called "random
> permutation" is not itself a permutation of anything. Rather, in some
> technical sense, it "contains" all finite permutations as "induced
> substructures". Furthermore, it is the unique smallest "structure" (this is
> a term of art from model theory) of the class of all finite permutations.
> This uniqueness, I think, is only up to isomorphism, so even if it were
> representable as, say, a permutation of the integers (and I don't think it
> is; I think it's a different kind of object), the representation wouldn't
> be unique.
>
>
> On Mon, Jun 22, 2015 at 12:03 PM, Neil Sloane <njasloane at gmail.com> wrote:
>
> > Dear Seq fans, there is a paper in the latest issue of
> > the Electronic J Combin, by Linman and Pinsker,
> > Permutations on the random permutation,
> > see http://www.combinatorics.org/ojs/index.php/eljc/issue/current
> >
> > They talk about THE random permutation as a unique well-defined thing.
> > It is the Fraissee limit of something ...
> >
> > My question is, if this really is unique and well-defined, what is it
> > and shouldn't it be in the OEIS?
> >
> > Maybe someone who is better educated in logic that I am can look into
> this?
> >
> >
> > Best regards
> > Neil
> >
> > 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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