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Double homotopy Cohen-Macaulayness for the poset of injective words and the classical NC-partition lattice

Abstract : 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.
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https://hal.inria.fr/hal-01215047
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Myrto Kallipoliti, Martina Kubitzke. Double homotopy Cohen-Macaulayness for the poset of injective words and the classical NC-partition lattice. 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.575-586. ⟨hal-01215047⟩

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