- the path ends at (n,n)
- the path may touch (but never goes over) the main diagonal
People have studied "generalized" Dyck paths, where the grid is now rectangular (n X m), and the step lengths are appropriately skewed. However, what I'm interested in is the following seemingly simple generalization:
Let a (n,k)-Dyck path be a Dyck path with the modification that the path, instead of ending at (n,n), ends at (n,k) (k <=n). What is the number of (n,k)-Dyck paths ?It seems like this should have been looked at, but I've been unable so far to find any reference to such a structure. I was wondering if readers had any pointers ? Note that this number is at most Cn-1 since any such path can be completed into a unique Dyck path.