✦ LIBER ✦

A Classic Proof of a Recurrence for a Very Classical Sequence

✍ Scribed by Dominique Foata; Doron Zeilberger

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 254 KB
Volume: 80
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.1997.2814

No coin nor oath required. For personal study only.

✦ Synopsis

has recently narrated the fascinating story of how the classical Schro der [Sch1870] numbers s(n) are even more classical than was previously believed. They (at least s(10)=103049) were known to Hipparchus (190 127 b.c.). Stanley recalled the three-term linear recurrence p. 57])

and stated that ``no direct combinatorial proof of this formula seems to be known.'' The purpose of this note is to fill this gap.

The present proof reflects the ideas of our great master, M.-P. Schu tzenberger (1920 1996), who taught us that every algebraic relation is to be given a combinatorial counterpart and vice versa. This methodology has been vigorously and successfully pursued by the E cole bordelaise (e.g., .

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