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math.CO2024
The ascent lattice on Dyck paths
Jean-Luc Baril, Mireille Bousquet-Mélou, Sergey Kirgizov +1
In the Stanley lattice defined on Dyck paths of size , cover relations are obtained by replacing a valley by a peak . We investigate a greedy version of this lattice, f…
math.CO2023
A lattice on Dyck paths close to the Tamari lattice
Jean-Luc Baril, Sergey Kirgizov, Mehdi Naima
We introduce a new poset structure on Dyck paths where the covering relation is a particular case of the relation inducing the Tamari lattice. We prove that the transitive closure…