[seqfan] Re: Table Matches "Connected Relations"

Richard J. Mathar mathar at mpia-hd.mpg.de
Thu Jun 13 10:23:19 CEST 2013


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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