Toward A "Universal Sequence Indicator" (USI)?

[Jon Awbrey]

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Paul Prueitt wrote:
>
> The transformation of the web site on integer sequences to a topic map "index"
> would face a couple of issues.  First of all sequences are mutually related by
> being "another sequences" but also by other kinds of relationships, some known
> and some unknown.  A major piece of number theory will have already gone into
> delineating the relationships between sequences.
>
> I would imagine that the average number of pair wise relationships might be 5 - 10.
> (Actually this number of relationships could go very high.)
> 
> Would anyone see a problem with this issue?
> 
> ***
> 
> Also I have a question:
> 
> Bernard said:
> 
> 4. "Author" should be another topic type, linked to sequences through
>    "authoring" associations.  (One question which is open in defining
>    such association types is the incidence of each role type:
>    one author or one sequence by association?)
> 
> Would you explain what you mean here by incidence of each role type ...
> in this context?
> 
> Perhaps this is the same question, but how might scope be used
> in a retrival or navigation task?
>
> _______________________________________________
> topicmapmail mailing list
> topicmapmail at infoloom.com
> http://www.infoloom.com/mailman/listinfo/topicmapmail

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Paul,

FYSMI ("funny you should mention it"), I just sent
a note off to the SeqFan List about this very topic,
which is short enough to copy here:

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Subj:  Universal Sequence Index (USI)?
Date:  Sat, 30 Jun 2001 12:34:01 -0400
From:  Jon Awbrey <jawbrey at oakland.edu>
  To:  Sequence Fanatics <seqfan at ext.jussieu.fr>

[ Nota Bene.  I had meant to write "Universal Sequence Indicator"
| but a long-entrained motor habit took possession of my fingers.
]

SeqFans,

Several recent notes have given me flashbacks to this old theme,
which I just realized how to express in more contemporary terms.
For some reason Marc's note makes me think of Conway's Fractran.

EIS is a resource that I will call "Lot_X", or "L_X" for short,
X being an index value to be named later.  I am tempted to let
X equal something between 1 and 7^2, but I do not know yet how
much of an initial segment might be needed for other resources.

I do not have a complete idea here, but here are a couple
of fragmentary ideas that may form the ingredients of one:

Ingredient 1.

If L_X^(L_A061396) = L_X^(L_A061396^1) is my initial sequence,
then the expression "L_X^(L_A061396^n)" might serve to denote
A061396's n-th element, although I don't want to fix this too
rigidly right yet as other ways of doing this may work better.

Ingredient 2.

Now, riffs are constituted in such a way as to yield a code value v(f)
for each finite partial function f : M -> M, where M = 1, 2, 3, 4, ...
Is there a good way of using this natural scheme to specify a sequence
in terms of references to other sequences, assuming that we can design
all the details of de/referencing to work out as elegantly as possible?
Exercise for the reader.  I'll think about it a bit and get back to you.

Jon Awbrey

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Data about "riffs" (rooted index-functional forests")
and cousin "rotes" (rooted odd trees with only exponent symmetries")
can be found at the following locations:

http://www.research.att.com/~njas/sequences/a061396.txt
http://www.research.att.com/~njas/sequences/a061396a.txt
http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A061396
http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A062504
http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A062860
http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A062537

I think that if one thinks about it one would realize, as I know that at least one did,
that this problem is much more generic vis-à-vis storing and finding hyperdata than it
may initially appear.

Jon Awbrey

P.S.  I am copying this note to Sloane and the SeqFan List, using BCC,
      not to be secretive or anything, but just to avoid bothering the
      busy beavers more than need B.
J.A.

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