[seqfan] Re: What is THE random permutation?

[Allan Wechsler]

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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