Search results for "Dyck and Motzkin paths"

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Dyck paths with a first return decomposition constrained by height

2018

International audience; We study the enumeration of Dyck paths having a first return decomposition with special properties based on a height constraint. We exhibit new restricted sets of Dyck paths counted by the Motzkin numbers, and we give a constructive bijection between these objects and Motzkin paths. As a byproduct, we provide a generating function for the number of Motzkin paths of height k with a flat (resp. with no flats) at the maximal height. (C) 2018 Elsevier B.V. All rights reserved.KeywordsKeyWords Plus:STATISTICS; STRINGS

Discrete mathematicsMathematics::CombinatoricsFirst return decompositionDyck and Motzkin pathsEnumerationHeightStatisticsGenerating function0102 computer and information sciences01 natural sciencesConstructiveTheoretical Computer ScienceConstraint (information theory)Combinatorics010104 statistics & probability010201 computation theory & mathematicsEnumerationBijectionDecomposition (computer science)Discrete Mathematics and CombinatoricsStrings0101 mathematics[MATH]Mathematics [math]MathematicsPeak
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