Abstract
We find a basis for the top homology of the non-crossing partition lattice T n . Though T n is not a geometric lattice, we are able to adapt techniques of Björner (A. Björner, On the homology of geometric lattices. Algebra Universalis 14 (1982), no. 1, 107–128) to find a basis with Cn−1 elements that are in bijection with binary trees. Then we analyze the action of the dihedral group on this basis.
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Zoque, E. A basis for the non-crossing partition lattice top homology. J Algebr Comb 23, 231–242 (2006). https://doi.org/10.1007/s10801-006-7395-5
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DOI: https://doi.org/10.1007/s10801-006-7395-5