A Classic Proof of a Recurrence for a Very Classical Sequence
Dominique Foata and
(Appeared in J. Comb. Theory-Ser.A 80(1997), 380-384.)
When Dominique Foata and I were working on our `main project' we
reached a stage where we desperately needed a distraction.
message advertising his latest
parking paper. When we downloaded it, we also found in his home page
the delightful and erudite historical
Schroeder-Hipparchus numbers, that contained a challenge: to supply
a "direct combinatorial proof" for the three-term linear recurrence
for these numbers.
This paper is dedicated to the memory of our great master
Marco Schutzenberger (20 Oct. 1920- 30 July 1996).
Comment Added Dec. 17, 1996: Laurent Habsieger came very close to
explaining the other mystery of Plutarch's sentence, where one counts
sentences with negatives allowed. His beautiful short note can be
Laurent Habsieger's Home Page
Comment Added Oct. 26, 1997: Bob Sulanke wrote a very intersting
article extending the presnt bijection
that appeared in J. Difference Eq. Appl. 5(1999), 155-176.
Doron Zeilberger's List of Papers
Doron Zeilberger's Home Page