| author: | Philippe Nadeau |
|---|---|
| title: | Walks reaching a line |
| keywords: | walk, generating function, rational language, singularity analysis |
| abstract: |
We enumerate walks in the plane
ℝ
, with steps East and North, that stop as soon as
they reach a given line; these walks are counted according
to the distance of the line to the origin, and we study the
asymptotic behavior when the line has a fixed slope and
moves away from the origin. When the line has a rational
slope, we study a more general class of walks, and give
exact as well as asymptotic enumerative results; for this,
we define a nice bijection from our walks to words of a
rational language. For a general slope, asymptotic results
are obtained; in this case, the method employed leads us to
find asymptotic results for a wider class of walks in
2
ℝ
.
m
|
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| reference: | Philippe Nadeau (2005), Walks reaching a line, in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 401-406 |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
| ps.gz-source: | dmAE0177.ps.gz (72 K) |
| ps-source: | dmAE0177.ps (201 K) |
| pdf-source: | dmAE0177.pdf (194 K) |
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