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

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https://doi.org/10.5070/C64264254Creative Commons 'BY' version 4.0 license
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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