Two bijections on Tamari Intervals
Abstrak
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.
Topik & Kata Kunci
Penulis (3)
Frédéric Chapoton
Gregory Chatel
Viviane Pons
Akses Cepat
- Tahun Terbit
- 2014
- Sumber Database
- DOAJ
- DOI
- 10.46298/dmtcs.2396
- Akses
- Open Access ✓