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On linear intervals in the alt \(\nu\)-Tamari lattices
Abstract
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
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