A basis for the non-crossing partition lattice top homology

Authors:
Eliana Zoque
Affiliations:
Departamento de Matemáticas, Universidad de los Andes, Bogotá, South America Carrera 1#18A-10
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
2006

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Abstract

We find a basis for the top homology of the non-crossing partition lattice Tn. Though Tn 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驴1 elements that are in bijection with binary trees. Then we analyze the action of the dihedral group on this basis.