Geometrically Constructed Bases for Homology of Non-Crossing Partition Lattices
نویسندگان
چکیده
منابع مشابه
Geometrically Constructed Bases for Homology of Non-Crossing Partition Lattices
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 .
متن کاملGeometrically Constructed Bases for Homology of Partition Lattices of Types A, B and D
We use the theory of hyperplane arrangements to construct natural bases for the homology of partition lattices of types A, B and D. This extends and explains the “splitting basis” for the homology of the partition lattice given in [20], thus answering a question asked by R. Stanley. More explicitly, the following general technique is presented and utilized. Let A be a central and essential hype...
متن کاملan 2 00 4 GEOMETRICALLY CONSTRUCTED BASES FOR HOMOLOGY OF PARTITION LATTICES OF TYPES
We use the theory of hyperplane arrangements to construct natural bases for the homology of partition lattices of types A, B and D. This extends and explains the " splitting basis " for the homology of the partition lattice given in [19], thus answering a question asked by R. Stanley. More explicitly, the following general technique is presented and utilized. Let A be a central and essential hy...
متن کاملA 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.
متن کاملNon-crossing Partition Lattices in Finite Real Reflection Groups
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2009
ISSN: 1077-8926
DOI: 10.37236/137