Geometrically Constructed Bases for Homology of Non-Crossing Partition Lattices
نویسنده
چکیده
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 .
منابع مشابه
Geometrically 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 کاملA degree bound for the Graver basis of non-saturated lattices
Let $L$ be a lattice in $ZZ^n$ of dimension $m$. We prove that there exist integer constants $D$ and $M$ which are basis-independent such that the total degree of any Graver element of $L$ is not greater than $m(n-m+1)MD$. The case $M=1$ occurs precisely when $L$ is saturated, and in this case the bound is a reformulation of a well-known bound given by several authors. As a corollary, we show t...
متن کاملCrossings and Nestings in Set Partitions of Classical Types
We study bijections { Set partitions of type X } −̃→ { Set partitions of type X } for X ∈ {A,B,C,D}, which preserve openers and closers. In types A, B, and C, they interchange • either the number of crossings and of nestings, • or the cardinalities of a maximal crossing and of a maximal nesting. In type D, the results are obtained only in the case of non-crossing and nonnesting set partitions. I...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 16 شماره
صفحات -
تاریخ انتشار 2009