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A Poset Fiber Theorem for Doubly Cohen-Macaulay Posets and Its Applications

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Abstract

This paper studies topological properties of the lattices of non-crossing partitions of types A and B and of the poset of injective words. Specifically, it is shown that after the removal of the bottom and top elements (if existent) these posets are doubly Cohen-Macaulay. This strengthens the well-known facts that these posets are Cohen-Macaulay. Our results rely on a new poset fiber theorem which turns out to be a useful tool to prove double (homotopy) Cohen- Macaulayness of a poset. Applications to complexes of injective words are also included.

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  1. Fakultät für Mathematik, Universität Wien, Garnisongasse 3, A-1090, Wien, Austria

    Myrto Kallipoliti & Martina Kubitzke

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  1. Myrto Kallipoliti
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  2. Martina Kubitzke
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Correspondence to Myrto Kallipoliti.

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Kallipoliti, M., Kubitzke, M. A Poset Fiber Theorem for Doubly Cohen-Macaulay Posets and Its Applications. Ann. Comb. 17, 711–731 (2013). https://doi.org/10.1007/s00026-013-0203-8

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