# Enumeration of walks reaching a line

Abstract : We enumerate walks in the plane $\mathbb{R}^2$, 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 $\mathbb{R}^m$.
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Communication dans un congrès
Stefan Felsner. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), pp.401-406, 2005, DMTCS Proceedings
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https://hal.inria.fr/hal-01184438
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Soumis le : lundi 17 août 2015 - 10:52:01
Dernière modification le : mardi 24 avril 2018 - 13:54:25
Document(s) archivé(s) le : mercredi 18 novembre 2015 - 10:35:17

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• HAL Id : hal-01184438, version 1

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Philippe Nadeau. Enumeration of walks reaching a line. Stefan Felsner. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), pp.401-406, 2005, DMTCS Proceedings. 〈hal-01184438〉

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