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A bijection on Dyck paths and its consequences

โœ Scribed by Emeric Deutsch

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
175 KB
Volume
179
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

A bijection is introduced in the set of all Dyck paths of semilength n from which it follows that (i) the parameters 'height of the first peak' and 'number of returns' have the same distribution and (ii) the parameter 'number of high peaks' has the Narayana distribution.

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In this paper, we introduce a subclass of the Dyck paths (Delest and Viennot, 1984) called nondecreasing Dyck paths which are enumerated by the Fibonacci numbers having odd indexes. We then use two different methods to enumerate these paths according to various parameters. By the first one, used in