Geometrically Constructed Bases for Homology of Partition Lattices of Types A, B and D

@article{Bjrner2004GeometricallyCB,
  title={Geometrically Constructed Bases for Homology of Partition Lattices of Types A, B and D},
  author={Anders Bj{\"o}rner and Michelle L. Wachs},
  journal={Electr. J. Comb.},
  year={2004},
  volume={11}
}
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 hyperplane arrangement in Rd. Let R1, . . . , Rk be the bounded regions of a generic hyperplane section of… CONTINUE READING

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References

Publications referenced by this paper.
Showing 1-10 of 29 references

Matroid shellability

G. M. Ziegler
β-systems, and affine hyperplane arrangements, J. Algebraic Combin. 1 (1992), 283–300. the electronic journal of combinatorics 11(2) • 2004
View 4 Excerpts
Highly Influenced

Basic Derivations for Subarrangements of Coxeter Arrangements

TADEUSZ JOZEFIAK, Bruce E. Sagan
2003
View 3 Excerpts
Highly Influenced

A basis for the homology of the d-divisible partition lattice

M. L. Wachs
Advances in Math. 117 • 1996
View 7 Excerpts
Highly Influenced

The face lattice of hyperplane arrangements

Discrete Mathematics • 1989
View 4 Excerpts
Highly Influenced

Higher multiplicities and almost free divisors and complete intersections

J. Damon
Memoirs Amer. Math. Soc. 589 • 1996
View 2 Excerpts
Highly Influenced

Facing up to arrangements: Face-count formulas for partitions of space by hyperplanes

T. Zaslavsky
Memoirs Amer. Math. Soc. 154 • 1975
View 3 Excerpts
Highly Influenced

The (Co)Homology of Lattices of Partitions with Restricted Block Size

A. E. Browdy
Ph.D. dissertation, University of Miami, 1996. the electronic journal of combinatorics 11(2) • 2004
View 1 Excerpt

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