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

@article{Zeilberger2012TheA, title={The Amazing \$3^n\$ Theorem and its even more Amazing Proof [Discovered by Xavier G. Viennot and his \'Ecole Bordelaise gang]}, author={Doron Zeilberger}, journal={arXiv: Combinatorics}, year={2012} }

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…

## 4 Citations

### Automated Counting of Towers (À La Bordelaise) [Or: Footnote to p. 81 of the Flajolet-Sedgewick Chef-d'œvre]

- Mathematics
- 2012

The brilliant idea of Jean Betrema and Jean-Guy Penaud that proved the celebrated "three to the power n" theorem of Dominique Gouyou-Beauchamps and Xavier Viennot, counting towers of domino pieces is…

### NSF Proposal: Automated Enumerative Combinatorics Automated Enumerative Combinatorics

- Computer Science
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My research students and I continued to practice a new research methodology, that can be loosely called rigorous experimental mathematics, that has something in common with both “mainstream” experimental mathematics (as preached by the Borwein brothers, David Bailey, Victor Moll, and their collaborators) and automated theorem proving, but is definitely distinct from them.

### Enumeration of $S$-omino towers and row-convex $k$-omino towers.

- Mathematics
- 2018

We first enumerate a generalization of domino towers that was proposed by Tricia M. Brown (J. Integer Seq. 20 (2017)), which we call S-omino towers. We establish equations that the generating…

### Algebraic and Geometric Methods in Enumerative Combinatorics

- Mathematics
- 2015

Enumerative combinatorics is about counting. The typical question is to find the number of objects with a given set of properties. However, enumerative combinatorics is not just about counting. In…

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