Dyck Paths and partial Bell polynomials

Toufik Mansour, Yidong Sun

Research output: Contribution to journalArticlepeer-review


In the present paper, we consider two kinds of statistics "number of u-segments" and "number of internal u-segments" in Dyck paths. More precisely, using Lagrange inversion formula we present the generating function for the number of Dyck paths according to semilength and our new statistics by the partial Bell polynomials, namely, where αr(D) (βr(D) is the number of w-segments (internal w-segments) of length r in a Dyck path D. Many important special cases are presented which lead to a lot of interesting results.

Original languageEnglish
Pages (from-to)285-297
Number of pages13
JournalAustralasian Journal of Combinatorics
StatePublished - 2008

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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