Results 31 to 40 of about 60 (45)
On the geometry of real or complex supersolvable line arrangements
Journal of Combinatorial Theory - Series A, 2016 Given a rank 3 real arrangement $\mathcal A$ of $n$ lines in the projective plane, the Dirac-Motzkin conjecture (proved by Green and Tao in 2013) states that for $n$ sufficiently large, the number of simple intersection points of $\mathcal A$ is greater than or equal to $n/2$.
Stefan O Tohaneanu, Benjamin Anzis
exaly +5 more sources
Free arrangements of hyperplanes and supersolvable lattices
Advances in Mathematics, 1984 The authors investigate the relation between two different concepts that come up with an arrangement A of hyperplanes through the origin in \({\mathbb{C}}^{\ell +1}\). On one hand, A is said to be free if the corresponding module of logarithmic vector fields is a free module.
Hiroaki Terao
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The Counting Polynomial of a Supersolvable Arrangement
Advances in Mathematics, 1995 Let \(A\) be an arrangement of hyperplanes in a real finite dimensional vector space \(V\). The components of the complement of the union of the hyperplanes are called the chambers of \(A\). The counting polynomial \(\sum_{i \geq 0} a_i t^i\) of \(A\) in a chamber \(C\) is defined by setting \(a_i\) equal to the number of chambers which are separated ...
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Supersolvable posets and fiber-type abelian arrangements
Selecta Mathematica, New SeriesAbstractWe present a combinatorial analysis of fiber bundles of generalized configuration spaces on connected abelian Lie groups. These bundles are akin to those of Fadell–Neuwirth for configuration spaces, and their existence is detected by a combinatorial property of an associated finite partially ordered set.
Christin Bibby
exaly +4 more sources
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Supersolvability of complementary signed-graphic hyperplane arrangements
Australas. J Comb., 2004The authors study the graphic arrangenment associated to complementary signed graphs consisting of positive and negative graphs such that their union is the complete graph (the reference on arrangements of hyperplanes is the book by \textit{P. Orlik} and \textit{H.
Guangfeng Jiang, Jianming Yu
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Lattice and order properties of the poset of regions in a hyperplane arrangement
Algebra Universalis, 2003Nathan Reading
exaly
Traversing regions of supersolvable hyperplane arrangements and their lattice quotients
Sofia Brenner +4 moreopenaire +2 more sources