1 research outputs found
Counting generalized Dyck paths
The Catalan number has a lot of interpretations and one of them is the number
of Dyck paths. A Dyck path is a lattice path from to which is
below the diagonal line . One way to generalize the definition of Dyck
path is to change the end point of Dyck path, i.e. we define (generalized) Dyck
path to be a lattice path from to which is
below the diagonal line , and denote by the number of
Dyck paths from to . In this paper, we give a formula to
calculate for arbitrary and .Comment: 15 pages, 2 figure