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Two combinatorial statistics on Dyck paths

โœ Scribed by Alain Denise; Rodica Simion

Book ID
103059154
Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
1003 KB
Volume
137
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

Two combinatorial statistics, the pyramid weight and the number of exterior pairs, are investigated on the set of Dyck paths. Explicit formulae are given for the generating functions of Dyck paths of prescribed pyramid weight and prescribed number of exterior pairs. The proofs are combinatorial and rely on the method of q-grammars as well as on two new q-analogues of the Catalan numbers derived from statistics on non-crossing partitions. Connections with the combinatorics of Motzkin paths are pointed out.

๐Ÿ“œ SIMILAR VOLUMES

A bijection on Dyck paths and its conseq
A bijection on Dyck paths and its consequences
โœ Emeric Deutsch ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 175 KB

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.