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Moscow Mathematical Journal, 2010, Volume 10, Number 3, Pages 611–628
DOI: https://doi.org/10.17323/1609-4514-2010-10-3-611-628 (Mi mmj395) 		 
This article is cited in 2 scientific papers (total 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
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DOI: https://doi.org/10.17323/1609-4514-2010-10-3-611-628
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.
Received: July 23, 2009; in revised form February 11, 2010
Bibliographic databases:
Document Type: Article
MSC: 05A16, 05A15
Language: English
Citation: V. R. Meshkov, A. V. Omelchenko, M. I. Petrov, E. A. Tropp, “Dyck and Motzkin triangles with multiplicities”, Mosc. Math. J., 10:3 (2010), 611–628
Citation in format AMSBIB
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\by V.~R.~Meshkov, A.~V.~Omelchenko, M.~I.~Petrov, E.~A.~Tropp
\paper Dyck and Motzkin triangles with multiplicities
\jour Mosc. Math.~J.
\yr 2010
\vol 10
\issue 3
\pages 611--628
\mathnet{http://mi.mathnet.ru/mmj395}
\crossref{https://doi.org/10.17323/1609-4514-2010-10-3-611-628}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2732576}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000281878900007}
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