[seqfan] Re: Table Matches "Connected Relations"

Ron Hardin rhhardin at att.net
Fri Jun 14 22:16:58 CEST 2013


It's nice to know there's some plausible connection to what it's connected to!

The table is now https://oeis.org/A226658

 rhhardin at mindspring.com
rhhardin at att.net (either)



----- Original Message ----
> From: Richard J. Mathar <mathar at mpia-hd.mpg.de>
> To: seqfan at seqfan.eu
> Sent: Thu, June 13, 2013 4:23:51 AM
> Subject: [seqfan] Re: Table Matches "Connected Relations"
> 
> In answer to http://list.seqfan.eu/pipermail/seqfan/2013-June/011288.html :
> 
> As (now) linked in A002501, Kreweras writes on page A578 of C. R.  Acad.
> Sc. (268) in 1969:
> 
> Le theoreme s'applique notamment au  denombrement des relation binaires
> externes qui possedent la propriete de  connexite; cela revient
> a calucule le nombre a(m,n) de manieres de replier un  tableu de m lignes
> et n colonnes avec des 0 et des 1, en respectant les deux  conditions
> suivantes:
>  1re: aucune range (ligne ni colonne) ne doit   etre tout entire remplie
>      de zeros;
>  2me: deux cases  quelconques marquees 1 peuvent etre jointes par une
>   chaine de cases  marqee 1 telle que deux cases consecutives de la chaine
>   appartiennet a  une meme rangee.
> 
> Stressing my French to the limit:
> So in a m-by-n  table of zeros and ones no row or column may be
> filled completely with zeros,  and
> for any two entries that contain 1's, they are connected by
> a chain of  1's such that two consecutive entries of the chain appear
> in the same  row.
> 
> So this is from where the "connected relations" get their  geometric
> interpretations.
> 
> Richard J.  Mathar
> 
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