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In geometry and combinatorics, an arrangement of hyperplanes is an arrangement of a finite set A of hyperplanes in a linear, affine, or projective space S. Questions about a hyperplane arrangement A generally concern geometrical, topological, or other properties of the complement, M(A), which is the set that remains when the hyperplanes are removed from the whole space. One may ask how these properties are related to the arrangement and its intersection semilattice. The intersection semilattice of A, written L(A), is the set of all subspaces that are obtained by intersecting some of the hyperplanes; among these subspaces are S itself, all the individual hyperplanes, all intersections of pairs of hyperplanes, etc. (excluding, in the affine case, the empty set). These intersection subspaces of A are also called the flats ofA. The intersection semilattice L(A) is partially ordered by reverse inclusion.
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References
- ↑ biographical information from American Men and Women of Science, Thomson Gale 2004
- 1 2 Conference in honour of Peter Orlik, Fields Institute, August 2008
- ↑ Peter Orlik at the Mathematics Genealogy Project
- ↑ Institute for Advanced Study: A Community of Scholars
- ↑ List of Fellows of the American Mathematical Society
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