[seqfan] Re: What is THE random permutation?

[Eric Angelini]

I _will_ consider during my sleep
(which starts... now!)

Catapulté de mon aPhone

> Le 26 juin 2015 à 00:34, Neil Sloane <njasloane at gmail.com> a écrit :
> 
> 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/
> 
> _______________________________________________
> 
> Seqfan Mailing list - http://list.seqfan.eu/