Generalized Schroder Numbers and the Rotation Principle

Given a point-lattice (m+1) ×(n+1) ⊆ N ×N and l ∈ N, we determine the number of royal paths from (0,0) to (m,n) with unit steps (1,0), (0,1) and (1,1), which never go below the line y = lx, by means of the rotation principle. Compared to the method of “penetrating analysis”, this principle has here the advantage of greater clarity and

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