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• W2010100934 abstract "This paper develops a unified enumerative and asymptotic theory of directed two-dimensional lattice paths in half-planes and quarter-planes. The lattice paths are specified by a finite set of rules that are both time and space homogeneous, and have a privileged direction of increase. (They are then essentially one-dimensional objects.) The theory relies on a specific “kernel method” that provides an important decomposition of the algebraic generating functions involved, as well as on a generic study of singularities of an associated algebraic curve. Consequences are precise computable estimates for the number of lattice paths of a given length under various constraints (bridges, excursions, meanders) as well as a characterization of the limit laws associated to several basic parameters of paths." @default.
• W2010100934 created "2016-06-24" @default.
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• W2010100934 date "2002-06-01" @default.
• W2010100934 modified "2023-10-16" @default.
• W2010100934 title "Basic analytic combinatorics of directed lattice paths" @default.
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• W2010100934 doi "https://doi.org/10.1016/s0304-3975(02)00007-5" @default.
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