A lattice on decreasing trees : the metasylvester lattice

Abstract : 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.
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Viviane Pons. A lattice on decreasing trees : the metasylvester lattice. 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), Jul 2015, Daejeon, South Korea. pp.381-392. ⟨hal-01337809⟩

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