Basic analytic combinatorics of directed lattice paths

@article{Banderier2002BasicAC,
  title={Basic analytic combinatorics of directed lattice paths},
  author={Cyril Banderier and Philippe Flajolet},
  journal={Theor. Comput. Sci.},
  year={2002},
  volume={281},
  pages={37-80}
}
This paper develops a uni(ed enumerative and asymptotic theory of directed two-dimensional lattice paths in half-planes and quarter-planes. The lattice paths are speci(ed by a (nite 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 speci(c “kernel method” that provides an important decomposition of the algebraic generating functions involved, as well as on a generic… CONTINUE READING
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