A Classic Proof of a Recurrence for a Very Classical Sequence
by Dominique Foata and Doron Zeilberger
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(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. Then arrived Richard Stanley's message advertising his latest parking paper. When we downloaded it, we also found in his home page the delightful and erudite historical paper about the 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 obtained from 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.

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