Geodesic
A basis for the non-crossing partition lattice top homology
Journal of Algebraic Combinatorics, Tome 23 (2006) no. 3, pp. 231-242.

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Summary: 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 $C _{ n - 1}$ elements that are in bijection with binary trees. Then we analyze the action of the dihedral group on this basis.
Keywords: keywords non-crossing partition, binary trees, homology group, Catalan numbers, representation matrix, dihedral group, stack-sortable permutations 
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     title = {A basis for the non-crossing partition lattice top homology},
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Zoque, Eliana. A basis for the non-crossing partition lattice top homology. Journal of Algebraic Combinatorics, Tome 23 (2006) no. 3, pp. 231-242. http://geodesic.mathdoc.fr/item/JAC_2006__23_3_a2/