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Catalan numbers revisited

✍ Scribed by Daniel Rubenstein

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 204 KB
Volume: 68
Category: Article
ISSN: 0097-3165
DOI: 10.1016/0097-3165(94)90119-8

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

On generalised catalan numbers

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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 gi

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It is known that a convex polygon of n sides admits C.-2 triangulations, where C, is a Catalan number. We classify these triangulations (considered as outerplanar graphs) according to their dual trees, and prove the following formula for the number of triangulations of a convex n-gon whose dual tree

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extended from N\* to Z\*. These extensions lead to Laurent series, 'special branches', and interesting formulas (including the 'Stirling Duality Law'). @