V. R. Meshkov, A. V. Omelchenko, M. I. Petrov, E. A. Tropp, “Dyck and Motzkin triangles with multiplicities”, Mosc. Math. J., 2010, Volume 10, Number 3,Pages <nobr>611

This article is cited in 2 papers

Dyck and Motzkin triangles with multiplicities

V. R. Meshkov, A. V. Omelchenko, M. I. Petrov, E. A. Tropp

St. Petersburg Academic University RAS, St. Petersburg, Russia

Abstract: 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.

Key words and phrases: Dyck and Motzkin triangles, Dyck and Motzkin paths, paths with multiplicities, exact enumeration of paths, generating function, asymptotic enumeration.

MSC: 05A16, 05A15

Received: July 23, 2009; in revised form February 11, 2010

Language: English

DOI: 10.17323/1609-4514-2010-10-3-611-628