[seqfan] Permutations of the natural numbers - subcategories needed?

Antti Karttunen antti.karttunen at gmail.com
Wed Apr 11 19:19:22 CEST 2018


Neil Sloane wrote in
http://list.seqfan.eu/pipermail/seqfan/2018-April/018575.html
in response to a question by Michel Marcus (
http://list.seqfan.eu/pipermail/seqfan/2018-April/018573.html )

> well of course ideally the best way is to use the Index entry

> permutations of the positive (or nonnegative) integers , sequences related
to :

> but that is probably not up to date

> To make it more up-to-date, we need to add more A-numbers to
> that Index, and we need to add more
> links to the Index from those A-numbers. Here is the link to add:

> <a href="/index/Per#IntegerPermutation">Index entries for sequences that
are permutations of the natural numbers</a>

> which I took from the classic permutation A006368.

My comment:

I think we need to create many subcategories under that category. I myself
have submitted (or infested, if you wish :-) OEIS with almost a thousand
permutations of natural numbers, and countless other people with many more.
Just listing those A-numbers, without even a possiblity to see their names
with mouse-hover-over wouldn't actually help at all compared to just
searching with
https://oeis.org/search?q=link%3Aintegerpermutation&sort=&language=&go=Search
(this gives 1766 entries, but I am sure there are many that have not
included the category-link).

So we would need to add some thought how to make a useful classification of
subcategories here (of course those subcategories do not need to be
mutually exclusive!).

E.g., I am myself fond of permutations that are usually simple mappings
based on various underlying combinatorial structures present either in the
prime (or other) factorization of n, or in some simple base-expansion
(base-2, Zeckendorf, etc). An example:
https://oeis.org/A273671
which involves Stern-Brocot tree and the exponents in prime factorization
of n interpreted in balanced binary expansion.
or https://oeis.org/A227351 which involves mapping between base-2 and
Fibonacci-representations of n.


On the other hand, many people prefer permutations based on some greedy
criteria, where a(n) is the least number such that it satisfies certain
criteria in respect to all the previous, or immediately previous,
especially if it is not (or was not) immediately obvious whether the
sequence actually is surjective and thus a permutation. (EKG-sequence, for
example, https://oeis.org/A064413 )

So, permutations involving greedy algorithm (and I think this could be
subdivided further), permutations involving prime factorization of n,
permutations based on base-2, -3, Fibonacci, Factorial, -10 expansion of n,
and so on? Any ideas?



Best regards,

Antti



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