Séminaire Lotharingien de Combinatoire, 89B.81 (2023), 12 pp.
Cesar Ceballos and Clément Chenevière
On Linear Intervals in the alt ν-Tamari Lattices
Abstract.
Given a lattice path ν, the ν-Tamari lattice and the ν-Dyck lattice are two natural examples of partial order structures on the set of lattice paths that lie weakly above ν.
In this paper, we introduce a more general family of lattices, called alt ν-Tamari lattices, which contains these two examples as particular cases. Unexpectedly, we show that all these lattices have the same number of linear intervals.
Received: November 15, 2022.
Accepted: February 20, 2023.
Final version: April 1, 2023.
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