A lattice on decreasing trees : the metasylvester lattice

Viviane Pons 1
1 GALaC - LRI - Graphes, Algorithmes et Combinatoire (LRI)
LRI - Laboratoire de Recherche en Informatique
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.
Type de document :
Communication dans un congrès
Formal Power Series and Algebraic Combinatorics , Jul 2015, Daejeon, South Korea. 27th Formal Power Series and Algebraic Combinatorics pp.12, 2015, 〈http://fpsac2015.sciencesconf.org/71002〉
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https://hal.inria.fr/hal-01284735
Contributeur : Viviane Pons <>
Soumis le : mardi 8 mars 2016 - 09:26:56
Dernière modification le : mardi 24 avril 2018 - 13:38:47

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  • HAL Id : hal-01284735, version 1
  • ARXIV : 1501.04868

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Viviane Pons. A lattice on decreasing trees : the metasylvester lattice. Formal Power Series and Algebraic Combinatorics , Jul 2015, Daejeon, South Korea. 27th Formal Power Series and Algebraic Combinatorics pp.12, 2015, 〈http://fpsac2015.sciencesconf.org/71002〉. 〈hal-01284735〉

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