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DTSTAMP:20230914T125920Z
SUMMARY:3^n
DESCRIPTION:Speaker: Xavier Viennot (LaBRI\nUniversity of Bordeaux 1\n33405
Talence Cedex\nFrance)\n\nAbstract: \nThe following is reproduced from Do
ron Zeilberger's page:\nhttp://www.math.rutgers.edu/~zeilberg/mamarim/mama
rimhtml/bordelaise.html.\nWe will (probably) never know the exact number o
f lattice animals with 1001 points\, but thanks to Xavier Viennot and Domi
nique Gouyou-Beauchamps we know\, exactly\, the number of directed animals
with compact source with that many points\, namely 31000\, since accordin
g to their amazing formula the answer for n+1 points is 3n. This is indeed
amazing\, since at first sight\, the second problem does not seem any eas
ier than the first.\nThe first proof of the 3n theorem\, by Gouyou-Beaucha
mps and Viennot\, that was published in 1988\, was a true tour-de-force\,
alas it was via a rather complicated (and seemingly ad hoc) bijection\, an
d Viennot believed that there must be a simpler proof.\nSo he invented his
famous empilements and his two Bordelaise disciples\, Jean Bétréma and
Jean-Guy Penaud\, used them to find the proof from the book\, (that anothe
r brilliant Bordelaise disciple\, Mireille Bousquet-Mélou\, taught me).\n
Alas this most elegant proof is buried in a long technical paper by Bétr
éma and Penaud\, and it is also buried in one of the almost one thousand
pages of the Flajolet-Sedgewick bible. It deserves to be better known! And
implemented!\nAnd guess what? By "combinatorial reverse-engineering" of t
his algebraic-combinatorial proof\, one can easily derive a natural biject
ion between these creatures (that I call xaviers) with n+1 pieces and word
s of length n in the alphabet {-1\,0\,1}\, that\, who knows?\, is similar
(or even the same!) as the old one\, but is much easier to formulate (and
program!).\n
URL:https://www.tcs.tifr.res.in/web/events/342
DTSTART;TZID=Asia/Kolkata:20130226T160000
DTEND;TZID=Asia/Kolkata:20130226T170000
LOCATION:AG-69
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