Tamari intervals and blossoming trees
We introduce a simple bijection between Tamari intervals and the blossoming trees (Poulalhon and Schaeffer, 2006) encoding planar triangulations, using a new meandering representation of such trees. Its specializations to the families of synchronized, Kreweras, new/modern, and infinitely modern intervals give a combinatorial proof of the counting formula for each family. Compared to (Bernardi and Bonichon, 2009), our bijection behaves well with the duality of Tamari intervals, also enabling the counting of self-dual intervals.Mathematics Subject Classifications: 05A15, 05A19Keywords: Tamari intervals, blossoming trees, enumeration, duality
Authors
- Éric Fusy
- Wenjie Fang (ORCID: https://orcid.org/0000-0001-9148-2807)
- Philippe Nadeau
Institutions
- Centre National de la Recherche Scientifique (FR)
- Laboratoire de Chimie Théorique (FR)
- Institut Camille Jordan (FR)
- Laboratoire d'Informatique Gaspard-Monge (FR)
- Université Gustave Eiffel (FR)
Publication Details
- Journal
- Combinatorial Theory
- Published
- 2025-03-14
- DOI
- https://doi.org/10.5070/c65165015
- Primary Topic
- African history and culture analysis
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Agence Nationale de la Recherche