Abstract:
An identity for generating functions is proved in this paper. A novel method to compute the number of restricted lattice paths is developed on the basis of this identity. The method employs a difference equation with non-constant coefficients. Dyck paths, Schröder paths, Motzkins path and other paths are computed to illustrate this method.
\Bibitem{Cha19}
\by Sreelatha~Chandragiri
\paper Difference equations and generating functions for some lattice path problems
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2019
\vol 12
\issue 5
\pages 551--559
\mathnet{http://mi.mathnet.ru/jsfu790}
\crossref{https://doi.org/10.17516/1997-1397-2019-12-5-551-559}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000501589200003}
Linking options:
https://www.mathnet.ru/eng/jsfu790
https://www.mathnet.ru/eng/jsfu/v12/i5/p551
This publication is cited in the following 4 articles:
S. Chandragiri, “Riordan Arrays and Difference Equations of Subdiagonal Lattice Paths”, Sib Math J, 65:2 (2024), 411
Svetlana S. Akhtamova, Tom Cuchta, Alexander P. Lyapin, “An Approach to Multidimensional Discrete Generating Series”, Mathematics, 12:1 (2024), 143
Sreelatha Chandragiri, “Counting lattice paths by using difference equations with non-constant coefficients”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 44 (2023), 55–70
Alexander P. Lyapin, Sreelatha Chandragiri, “The Cauchy problem for multidimensional difference equations in lattice cones”, Zhurn. SFU. Ser. Matem. i fiz., 13:2 (2020), 187–196
Citation in format AMSBIB
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