# [seqfan] Re: True (?) reordering

Marc LeBrun mlb at well.com
Fri Mar 5 18:43:07 CET 2010

```Derangement?  http://en.wikipedia.org/wiki/Derangement

BTW we might want to be careful with this terminology.  I think of
"reordering" or "ordering" as a distinctly different, and weaker, concept,
distinct from "permutation".  An ordering defines a predicate [<] on NxN,
whereas a permutation defines a map n --> a(n).  Every permutation is an
ordering, but not vice versa.  Lovely example:

http://mathworld.wolfram.com/SharkovskysTheorem.html

(apropos which Freeman Dyson said, on the subject of chaos, "I know only one
rigorous theorem" http://www.ams.org/notices/200902/rtx090200212p.pdf )

>="Eric Angelini" <Eric.Angelini at kntv.be>

>
> Hello SeqFans,
>
> when one reads in the OEIS something like:
> "A reordering of the natural numbers", does
> this mean that we never have n = a(n) in
> the reordered sequence? If not, is there a
> name/concept for that?
>
> Best,
> É.
>
> ------------------------
> An example is given here:
>
> (Original wording by Frans Faase):
>
>> If you would send the letters of the alphabet in the alphabetic order using
>> the morse code you get a sequence of 82 dots and stripes. How many
>> non-alphabetic orderings of the letters of the alphabet exists, which when
>> send in morse code would result in the same sequence (ignoring the pauzes
>> between individual letters)?
>
> Frans has found 48 reorderings -- but only
> the last eight, here, show no letter at its
> original place -- thus a "true" (?) reodering:
>
> PFCHNZSVORXMJWAKLUIBYDQTGE
> PFCHNZSVORXQTYWALUIBKGEMJD
> PFCHNZSVORXQTYEMALUIBKGWJD
> PFCHNZSVORXQGTYALUIBKMEWJD
> PFCHTEZSVORXQGMAKLUIBYNWJD
> PFCHNZSVORXQGMAKLUIBYTEWJD
> PFCHNZSVORXGTQYALUIBKMEWJD
> PFCHNZSVORXMAQYETLUIBKGWJD
> PFCHNZSVORXMETQYALUIBKGWJD
> PFCHNZSVORXMAGQKLUIBYTEWJD
> PFCHNZSVTQEXGMYWRBLDAJUKOI
> PFCHNZSVORXQMAYETLUIBKGWJD
> PFCHNZSVORXQMETYALUIBKGWJD
> PFCHTEZSVORXMAGQKLUIBYNWJD
> WVRBUPSHOCXQGTYALFENIKZMJD
> WVRBUPSHOCXGTQYALFENIKZMJD
> PFTLSNZHUORXQMAYECVIBKGWJD
> PFTLVWIHUMCNJAQYRBEXSKZGOD
> PFTLVWIHUMNCJAQYRBEXSKZGOD
> PFTLSNZHUORXMAQYECVIBKGWJD
> PFKIVEZHUORXQGMACTSLBYNWJD
> PFKIVEZHUORXQGMACBLTSYNWJD
> PFKIVEZHUORXMAGQCTSLBYNWJD
> PFKIVEZHUORXMAGQCBLTSYNWJD
> PFKHRZSVMCXQTYWAEBLNUJIGOD
> PFKHAEZSVMCXQTYWRBLNUJIGOD
> PFKHRZSVTQEXMWYACBLNUJIGOD
> PFKIVWHSEOCXGTQYRBLNUAZMJD
> PFKIVWHESOCXGTQYRBLNUAZMJD
> PFKIVWSHEOCXGTQYRBLNUAZMJD
> PFKIVWSEHOCXGTQYRBLNUAZMJD
> PFKIVWESHOCXGTQYRBLNUAZMJD
> PFKIVWHSEOCXQGTYRBLNUAZMJD
> PFKIVWHESOCXQGTYRBLNUAZMJD
> PFKIVWSHEOCXQGTYRBLNUAZMJD
> PFKIVWSEHOCXQGTYRBLNUAZMJD
> PFKIVWESHOCXQGTYRBLNUAZMJD
> EGFKIVPSHOCXQTYWRBLNUAZMJD
> WEFKIVPSHOCXQGTYRBLNUAZMJD
> WEFKIVPSHOCXGTQYRBLNUAZMJD
> WVENBUPSHOCXQGTYALFRIKZMJD
> WVENBUPSHOCXGTQYALFRIKZMJD
> WVRNIUPSHOCXQGTYALFEBKZMJD
> WVRNIUPSHOCXGTQYALFEBKZMJD
> PFKHRZSVMCXQGTYALUIBNOEWJD
> PFKHRZSVMCXGTQYALUIBNOEWJD
> PFTLVWHIUMCNJAQYRBEXSKZGOD
> PFTLVWHIUMNCJAQYRBEXSKZGOD
>
> See here, in colour:
> Best,
> É.
>
>
>
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

```