Combinatorial Theory

Given a lattice path $\nu$, the $\nu$-Tamari lattice and the $\nu$-Dyck lattice are two natural examples of partial order structures on the set of lattice paths that lie weakly above $\nu$. In this paper, we introduce a more general family of lattices, called alt $\nu$-Tamari lattices, which contains these two examples as particular cases. Unexpectedly, we show that all these lattices have the same number of linear intervals.

Mathematics Subject Classifications: 06A07, 06B05, 05A19

Keywords: Lattices, intervals, Tamari