The Amazing $3^n$ Theorem and its even more Amazing Proof [Discovered by Xavier G. Viennot and his École Bordelaise gang]

• Published in 2012
• Added on 2021-03-15

The most amazing (at least to me) result in Enumerative Combinatorics is Dominique Gouyou-Beauchamps and Xavier Viennot's theorem that states that the number of so-called directed animals with compact source (that are equivalent, via Viennot's beautiful concept of heaps, to towers of dominoes, that I take the liberty of renaming xaviers) with n+1 points equals 3^n. This amazing result received an even more amazing proof by Jean B\'etrema and Jean-Guy Penaud. Both theorem and proof deserve to be better known! Hence this article, that is also accompanied by a comprehensive Maple package http://www.math.rutgers.edu/~zeilberg/tokhniot/BORDELAISE that implements everything (and much more)

Links

• http://arxiv.org/abs/1208.2258v1
• http://arxiv.org/pdf/1208.2258v1

Other information

BibTeX entry

@article{TheAmazing3nTheoremanditsevenmoreAmazingProofDiscoveredbyXavierGViennotandhiscoleBordelaisegang,
	key = {TheAmazing3nTheoremanditsevenmoreAmazingProofDiscoveredbyXavierGViennotandhiscoleBordelaisegang},
	type = {article},
	title = {The Amazing {\$}3^n{\$} Theorem and its even more Amazing Proof [Discovered by  Xavier G. Viennot and his {\'{E}}cole Bordelaise gang]},
	author = {Doron Zeilberger},
	abstract = {The most amazing (at least to me) result in Enumerative Combinatorics is
Dominique Gouyou-Beauchamps and Xavier Viennot's theorem that states that the
number of so-called directed animals with compact source (that are equivalent,
via Viennot's beautiful concept of heaps, to towers of dominoes, that I take
the liberty of renaming xaviers) with n+1 points equals 3^n. This amazing
result received an even more amazing proof by Jean B\'etrema and Jean-Guy
Penaud. Both theorem and proof deserve to be better known! Hence this article,
that is also accompanied by a comprehensive Maple package
http://www.math.rutgers.edu/{\~{}}zeilberg/tokhniot/BORDELAISE that implements
everything (and much more)},
	comment = {},
	date_added = {2021-03-15},
	date_published = {2012-12-07},
	urls = {http://arxiv.org/abs/1208.2258v1,http://arxiv.org/pdf/1208.2258v1},
	collections = {attention-grabbing-titles,combinatorics,fun-maths-facts,things-to-make-and-do},
	url = {http://arxiv.org/abs/1208.2258v1 http://arxiv.org/pdf/1208.2258v1},
	year = 2012,
	urldate = {2021-03-15},
	archivePrefix = {arXiv},
	eprint = {1208.2258},
	primaryClass = {math.CO}
}