[seqfan] Re: What is THE random permutation?

[Neil Sloane]

PS Well, what if we try to build our own version?
We look for an infinite sequence of natural numbers, with repeats.
Call it S_infinity.  This will be the limiting sequence of S_1, S_2, S_3,...
We have:

S_1 = 1

S_2 = 121

S_3 is (perhaps) 1213212312

The rules for finding S_n are:

   1. S_n must begin with S_{n-1}

   2. Every one of the n! permutations of 1..n must appear somewhere
   in a width-n window in S_n

   3. Out of all S_n satisfying 1. and 2. pick the lexicographically
earliest

Or something like that!  Eric Angelini, is this something you might
have considered?

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 6:02 PM, Neil Sloane <njasloane at gmail.com> wrote:

> 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
>> >
>> > _______________________________________________
>> >
>> > Seqfan Mailing list - http://list.seqfan.eu/
>> >
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>
>