Viviane Pons
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A lattice on decreasing trees : the metasylvester lattice
dmtcs:2523 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2015,
DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
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https://doi.org/10.46298/dmtcs.2523
A lattice on decreasing trees : the metasylvester latticeConference paper
Authors: Viviane Pons 1
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Viviane Pons
1 Graphes, Algorithmes et Combinatoire (LRI)
We introduce a new combinatorial structure: the metasylvester lattice on decreasing trees. It appears in the context of the m-Tamari lattices and other related m-generalizations. The metasylvester congruence has been recently introduced by Novelli and Thibon. We show that it defines a sublattice of the m-permutations where elements can be represented by decreasing labelled trees: the metasylvester lattice. We study the combinatorial properties of this new structure. In particular, we give different realizations of the lattice. The m-Tamari lattice is by definition a sublattice of our newly defined metasylvester lattice. It leads us to a new realization of the m-Tamari lattice, using certain chains of the classical Tamari lattice.