Myrto Kallipoliti ; Henri Mühle - The m-Cover Posets and the Strip-Decomposition of m-Dyck Paths

dmtcs:2409 - Discrete Mathematics & Theoretical Computer Science, January 1, 2014, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014) - https://doi.org/10.46298/dmtcs.2409
The m-Cover Posets and the Strip-Decomposition of m-Dyck PathsConference paper

Authors: Myrto Kallipoliti ORCID1; Henri Mühle 1

  • 1 Fakultät für Mathematik [Wien]

In the first part of this article we present a realization of the m-Tamari lattice T(m)n in terms of m-tuples of Dyck paths of height n, equipped with componentwise rotation order. For that, we define the m-cover poset Pm of an arbitrary bounded poset P, and show that the smallest lattice completion of the m-cover poset of the Tamari lattice Tn is isomorphic to the m-Tamari lattice T(m)n. A crucial tool for the proof of this isomorphism is a decomposition of m-Dyck paths into m-tuples of classical Dyck paths, which we call the strip-decomposition. Subsequently, we characterize the cases where the m-cover poset of an arbitrary poset is a lattice. Finally, we show that the m-cover poset of the Cambrian lattice of the dihedral group is a trim lattice with cardinality equal to the generalized Fuss-Catalan number of the dihedral group.


Volume: DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
Section: Proceedings
Published on: January 1, 2014
Imported on: November 21, 2016
Keywords: m-Tamari lattice,m-Dyck paths,m-cover poset,Fuss-Catalan combinatorics,Symmetric group,Dihedral group,Left-modularity,Trimness,Möbius function,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
Funding:
    Source : OpenAIRE Graph
  • Klassische Kombinatorik und Anwendungen; Code: Z 130

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