Enumerating closed flows on forks

The flows on rooted trees were recently introduced in the study of the free Pre-Lie group. In this paper, we establish a bijection between the closed flows on specific rooted trees called forks and the classical ballot paths. As a consequence, an enumeration formula conjectured by F. Chapoton is bij...

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Bibliographic Details
Published inDiscrete mathematics Vol. 340; no. 12; pp. 3002 - 3010
Main Author Su, Xun-Tuan
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2017
Subjects
Ballot paths
Closed flows
Matching paths
NE-turns
Rooted trees
Closed flows
Matching paths
Ballot paths
Rooted trees
NE-turns
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Summary:The flows on rooted trees were recently introduced in the study of the free Pre-Lie group. In this paper, we establish a bijection between the closed flows on specific rooted trees called forks and the classical ballot paths. As a consequence, an enumeration formula conjectured by F. Chapoton is bijectively proved.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2017.07.014