[seqfan] Re: True (?) reordering

[Eric Angelini]

Charles Greathouse:
> Derangement 

... yes, this is it, thank you Charles!
http://mathworld.wolfram.com/Derangement.html
Best,
É.


-----Message d'origine-----
De : seqfan-bounces at list.seqfan.eu
[mailto:seqfan-bounces at list.seqfan.eu] 
De la part de Eric Angelini
Envoyé : vendredi 5 mars 2010 17:11
À : Sequence Fanatics Discussion list
Objet : [seqfan] True (?) reordering


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:
http://www.cetteadressecomportecinquantesignes.com/Faase.htm
Best,
É.



 


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