Myrto Kallipoliti ; Martina Kubitzke - Double homotopy Cohen-Macaulayness for the poset of injective words and the classical NC-partition lattice

dmtcs:2935 - Discrete Mathematics & Theoretical Computer Science, January 1, 2011, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) - https://doi.org/10.46298/dmtcs.2935
Double homotopy Cohen-Macaulayness for the poset of injective words and the classical NC-partition lattice

Authors: Myrto Kallipoliti ; Martina Kubitzke

    In this paper we study topological properties of the poset of injective words and the lattice of classical non-crossing partitions. Specifically, it is shown that after the removal of the bottom and top elements (if existent) these posets are doubly Cohen-Macaulay. This extends the well-known result that those posets are shellable. Both results rely on a new poset fiber theorem, for doubly homotopy Cohen-Macaulay posets, which can be considered as an extension of the classical poset fiber theorem for homotopy Cohen-Macaulay posets.


    Volume: DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
    Section: Proceedings
    Published on: January 1, 2011
    Imported on: January 31, 2017
    Keywords: injective words,non-crossing partitions,strongly constructible,doubly homotopy Cohen-Macaulay,poset fiber theorem,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
    Fundings :
      Source : OpenAIRE Research Graph
    • Compact enumeration formulas for generalized partitions; Funder: Austrian Science Fund (FWF); Code: Y 463

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