Dyck paths and partial Bell polynomials
نویسندگان
چکیده
In the present paper, we consider two kinds of statistics “number of usegments” 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, ∑ D∈Dn ∏ i≥1 t αi(D) i = n ∑ i=1 1 (n− i+ 1)!n,i ( 1!t1, 2!t2, · · · ) , ∑ D∈Dn ∏ i≥1 t βi(D) i = n ∑
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ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 42 شماره
صفحات -
تاریخ انتشار 2008