HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Conference papers

Two bijections on Tamari Intervals

Abstract : We use a recently introduced combinatorial object, the $\textit{interval-poset}$, to describe two bijections on intervals of the Tamari lattice. Both bijections give a combinatorial proof of some previously known results. The first one is an inner bijection between Tamari intervals that exchanges the $\textit{initial rise}$ and $\textit{lower contacts}$ statistics. Those were introduced by Bousquet-Mélou, Fusy, and Préville-Ratelle who proved they were symmetrically distributed but had no combinatorial explanation. The second bijection sends a Tamari interval to a closed flow of an ordered forest. These combinatorial objects were studied by Chapoton in the context of the Pre-Lie operad and the connection with the Tamari order was still unclear.
Complete list of metadata

Cited literature [9 references]  Display  Hide  Download

Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Thursday, October 1, 2015 - 9:29:01 AM
Last modification on : Saturday, January 15, 2022 - 3:57:59 AM
Long-term archiving on: : Saturday, January 2, 2016 - 10:52:44 AM


Publisher files allowed on an open archive



Frédéric Chapoton, Grégory Chatel, Viviane Pons. Two bijections on Tamari Intervals. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. pp.241-252, ⟨10.46298/dmtcs.2396⟩. ⟨hal-01207596⟩



Record views


Files downloads