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

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

2011-01-30

arxiv.org/abs/1101.5770v2

Mathematics

Combinatorics

16 pages, 3 figures

Scientific paper

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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