A poset fiber theorem for doubly Cohen-Macaulay posets and its applications to non-crossing partitions and injective words

Myrto Kallipoliti; Martina Kubitzke

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arXiv · 1101.5770

A poset fiber theorem for doubly Cohen-Macaulay posets and its applications to non-crossing partitions and injective words

Myrto Kallipoliti·Martina Kubitzke

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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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Myrto Kallipoliti, Martina Kubitzke. 2011-04-12. A poset fiber theorem for doubly Cohen-Macaulay posets and its applications to non-crossing partitions and injective words. https://arxiv.org/abs/1101.5770

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