✦ LIBER ✦

On generalised catalan numbers

✍ Scribed by A.D. Sands

Publisher: Elsevier Science
Year: 1978
Tongue: English
Weight: 549 KB
Volume: 21
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(78)90094-8

No coin nor oath required. For personal study only.

✦ Synopsis

The Catalan numb;r C, is defined to be 2n

( >I (n + 1). One of its occurrences is as the n number of ways of bracketing a product of n + 1 terms taken from a set with binaqr operation. In. this note the corresponding result for a set with a k-ary operation is considered. A combinatorial proof is given which does not involve generating functions or inversion formulae. The result is further ~~neralised to obtain a simpler proof of a formula of Erdelyi and Etherington [2], interpreted here as a result coscerning a set with several k,-ary operations.

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