[seqfan] Permutations (Was: Evaluating sequences by same terms and different indices)

[Antti Karttunen]

On Sun, Mar 8, 2015 at 12:33 AM,  <seqfan-request at list.seqfan.eu> wrote:

> Message: 3
> Date: Thu, 5 Mar 2015 21:39:13 -0600
> From: "Bob Selcoe" <rselcoe at entouchonline.net>
> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
> Subject: [seqfan] Re: Evaluating sequences by same terms and different
>         indices
> Message-ID: <D8F38AB413E046BFA770495A115CEF1D at OwnerPC>
> Content-Type: text/plain; format=flowed; charset="utf-8";
>         reply-type=original
>
> Hi Frank,
>
> Thanks for the reply.  The issue isn't how to show the indexing; it's to
> describe the comparisons.
>
> For instance, A064413 and A255582.  What would f and g be that would express
> their similarity?  What are the "explicit formulas"??

Submit for example a(n) = A064413(A255479(n)) [where A255479 is the
inverse permutation of A255582] and also its inverse b(n) =
A255582(A064664(n)) [where A064664 is the inverse of A064413]. If the
resulting graphs stay "near" the diagonal y=x, then the permutations
A064413 and A255582 are quite "similar" in some respect. Also, find
the fixed points of a [equally, the fixed points of its inverse b],
i.e. those n for which a(n) = n.

This has in general proved to be a good technique of finding
interesting new sequences. First I'm just slightly irritated by some
common property of two sequences, permutations or tables, and almost
brush it aside as an irrelevant coincidence, but then, when I start
computing sequences based on that, suddenly something interesting can
be found.
For a quite recent example, see e.g.:
https://oeis.org/A241912
and
https://oeis.org/A249821


Best regards,

Antti



>
> Bob S
>
> --------------------------------------------------
> From: "Frank Adams-Watters" <franktaw at netscape.net>
> Sent: Thursday, March 05, 2015 7:34 PM
> To: <seqfan at list.seqfan.eu>
> Subject: [seqfan] Re: Evaluating sequences by same terms and
> differentindices
>
>> I don't quite see the problem. You can enter a formula like:
>>
>> a(f(n)) = b(n) or a(n) = b(g(n)) or even a(f(n)) = b(g(n))
>>
>> (where f and g are explicit formulas, and b is an A-number).
>>
>> What further description do you need?
>>
>> Franklin T. Adams-Watters
>>