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

By
Shalosh B. Ekhad and Doron Zeilberger

.pdf   .ps   .tex  

Written: 12/12/12 (i.e. Dec. 12, 2012)

(Exclusively published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger and arxiv.org)


Pour Philippe FLAJOLET (1948-2011), In Memoriam
When a good idea can make something that, a priori, seemed "deep", into something that, a posteriori, turned out to be trivial (or almost so), it usually can be used to also derive many new results that, even a posteriori, are highly non-trivial, but, of course, with the kind help of our silicon brethern.

This is the case with the Bétréma - Penaud brilliant idea that one of us (DZ) talked about here, and realized that the same argument can be used to enumerate much more general towers. Then the other one of us (SBE) found lots of new deep results (see the output files below).


Maple Package


Sample Input and Output for the Maple package TOWERS


Personal Journal of Shalosh B. Ekhad and Doron Zeilberger

Doron Zeilberger's Home Page