6533b85ffe1ef96bd12c1c5e
RESEARCH PRODUCT
Dyck paths with a first return decomposition constrained by height
Sergey KirgizovJean-luc BarilArmen Petrossiansubject
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]MathematicsPeakdescription
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
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-06-01 |