Difference equations and generating functions for some lattice path problems
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 5, pp. 551-559
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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.
Keywords:
difference equation, generating function, lattice path.
@article{JSFU_2019_12_5_a2,
author = {Sreelatha Chandragiri},
title = {Difference equations and generating functions for some lattice path problems},
journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
pages = {551--559},
publisher = {mathdoc},
volume = {12},
number = {5},
year = {2019},
language = {en},
url = {http://geodesic.mathdoc.fr/item/JSFU_2019_12_5_a2/}
}
TY - JOUR AU - Sreelatha Chandragiri TI - Difference equations and generating functions for some lattice path problems JO - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika PY - 2019 SP - 551 EP - 559 VL - 12 IS - 5 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/JSFU_2019_12_5_a2/ LA - en ID - JSFU_2019_12_5_a2 ER -
%0 Journal Article %A Sreelatha Chandragiri %T Difference equations and generating functions for some lattice path problems %J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika %D 2019 %P 551-559 %V 12 %N 5 %I mathdoc %U http://geodesic.mathdoc.fr/item/JSFU_2019_12_5_a2/ %G en %F JSFU_2019_12_5_a2
Sreelatha Chandragiri. Difference equations and generating functions for some lattice path problems. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 5, pp. 551-559. http://geodesic.mathdoc.fr/item/JSFU_2019_12_5_a2/