Pattern-avoiding Dyck paths
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Published:2013-01-01
Issue:Proceedings
Volume:DMTCS Proceedings vol. AS,...
Page:
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ISSN:1365-8050
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Container-title:Discrete Mathematics & Theoretical Computer Science
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language:en
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Short-container-title:
Author:
Bernini Antonio,Ferrari Luca,Pinzani Renzo,West Julian
Abstract
International audience
We introduce the notion of $\textit{pattern}$ in the context of lattice paths, and investigate it in the specific case of Dyck paths. Similarly to the case of permutations, the pattern-containment relation defines a poset structure on the set of all Dyck paths, which we call the $\textit{Dyck pattern poset}$. Given a Dyck path $P$, we determine a formula for the number of Dyck paths covered by $P$, as well as for the number of Dyck paths covering $P$. We then address some typical pattern-avoidance issues, enumerating some classes of pattern-avoiding Dyck paths. Finally, we offer a conjecture concerning the asymptotic behavior of the sequence counting Dyck paths avoiding a generic pattern and we pose a series of open problems regarding the structure of the Dyck pattern poset.
Publisher
Centre pour la Communication Scientifique Directe (CCSD)
Subject
Discrete Mathematics and Combinatorics,General Computer Science,Theoretical Computer Science
Cited by
1 articles.
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