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 latticeArticle

Authors: Myrto Kallipoliti ORCID1,2; Martina Kubitzke 3

  • 1 Department of Mathematics [Athens]
  • 2 Erwin Schrödinger Institute for Mathematical Physics
  • 3 Fakultät für Mathematik [Wien]

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.

https://doi.org/10.46298/dmtcs.2935
Source: HAL:hal-01215047v1
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]
Funding:
    Source : OpenAIRE Graph
  • Compact enumeration formulas for generalized partitions; Code: Y 463

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