Skip to Main content Skip to Navigation
Conference papers

Counting smaller trees in the Tamari order

Abstract : We introduce new combinatorial objects, the interval-posets, that encode intervals of the Tamari lattice. We then find a combinatorial interpretation of the bilinear form that appears in the functional equation of Tamari intervals described by Chapoton. Thus, we retrieve this functional equation and prove that the polynomial recursively computed from the bilinear form on each tree $T$ counts the number of trees smaller than $T$ in the Tamari order.
Document type :
Conference papers
Complete list of metadata

Cited literature [8 references]  Display  Hide  Download
Contributor : Alain Monteil Connect in order to contact the contributor
Submitted on : Tuesday, November 17, 2015 - 10:20:54 AM
Last modification on : Saturday, January 15, 2022 - 3:58:19 AM
Long-term archiving on: : Friday, April 28, 2017 - 5:13:51 PM


Publisher files allowed on an open archive


  • HAL Id : hal-00824154, version 2



Grégory Chatel, Viviane Pons. Counting smaller trees in the Tamari order. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. pp.433-444. ⟨hal-00824154v2⟩



Record views


Files downloads