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.
|Number of pages||13|
|Journal||Australasian Journal of Combinatorics|
|State||Published - 2008|
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics