On maximal chains in the non-crossing partition lattice
نویسندگان
چکیده
منابع مشابه
A basis for the non-crossing partition lattice top homology
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−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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For a finite real reflection group W with Coxeter element γ we give a case-free proof that the closed interval, [I, γ], forms a lattice in the partial order on W induced by reflection length. Key to this is the construction of an isomorphic lattice of spherical simplicial complexes. We also prove that the greatest element in this latter lattice embeds in the type W simplicial generalised associ...
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For any finite, real reflection group W , we construct a geometric basis for the homology of the corresponding non-crossing partition lattice. We relate this to the basis for the homology of the corresponding intersection lattice introduced by Björner and Wachs in [4] using a general construction of a generic affine hyperplane for the central hyperplane arrangement defined by W .
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2014
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2014.02.002