Automated Counting of Towers (\`A La Bordelaise) [Or: Footnote to p. 81 of the Flajolet-Sedgewick Chef-d'{\oe}vre]
Shalosh B. Ekhad, Doron Zeilberger
TL;DR
This paper extends a combinatorial method for counting towers of domino pieces to more general towers with various i-mers, building on a celebrated theorem and demonstrating broader enumeration capabilities.
Contribution
It introduces a generalized approach for enumerating towers of various i-mers, expanding the original domino tower counting method.
Findings
Extended the original domino tower enumeration to general i-mers.
Proved a broader class of towers can be counted using the extended method.
Connected the enumeration to the 'three to the power n' theorem of Gouyou-Beauchamps and Viennot.
Abstract
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 extended and used to enumerate much more general towers, where the pieces can be many i-mers.
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Taxonomy
TopicsImage Processing and 3D Reconstruction · Topological and Geometric Data Analysis · Mathematical Dynamics and Fractals