vix.ing · top · new · best · stats · spec

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

2012/08/10 by Doron Zeilberger, Zeilberger, Doron
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #Data Management and Algorithms #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1208.2258

6 pages

arxiv created 2012/08/10 · openalex publication_date 2012/08/10 · arxiv updated 2012/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 3n. This amazing result received an even more amazing proof by Jean Bétrema 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)

Related