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# A lattice on decreasing trees : the metasylvester lattice

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.
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Conference papers
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https://hal.archives-ouvertes.fr/hal-01337809
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Submitted on : Monday, June 27, 2016 - 3:23:18 PM
Last modification on : Wednesday, September 16, 2020 - 5:45:43 PM

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Poster6.pdf
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### Licence

Distributed under a Creative Commons Attribution 4.0 International License

### Identifiers

• HAL Id : hal-01337809, version 1
• ARXIV : 1501.04868

### Citation

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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