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Regular version of the site

Article

Dyck and Motzkin Triangles with Multiplicities

Moscow Mathematical Journal. 2010. Vol. 10. No. 3. P. 611-628.
A. Omelchenko, Meshkov V., Petrov M., Tropp E.

Exponential generating functions for the Dyck and Motzkin triangles are constructed for various assignments of multiplicities to the arrows of these triangles. The possibility to build such a function provided that the generating function for paths that end on the axis is a priori unknown is analyzed. Asymptotic estimates for the number of paths are obtained for large values of the path length.