Results 1 to 10 of about 57 (42)
Supersolvable orders and inductively free arrangements
Open Mathematics, 2017 In this paper, we define the supersolvable order of hyperplanes in a supersolvable arrangement, and obtain a class of inductively free arrangements according to this order.
Ruimei Gao
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Gallery Posets of Supersolvable Arrangements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We introduce a poset structure on the reduced galleries in a supersolvable arrangement of hyperplanes. In particular, for Coxeter groups of type A or B, we construct a poset of reduced words for the longest element whose Hasse diagram is the graph of ...
Thomas McConville
doaj +4 more sources
Supersolvable simplicial arrangements [PDF]
Advances in Applied Mathematics, 2019 Simplicial arrangements are classical objects in discrete geometry. Their classification remains an open problem but there is a list conjectured to be complete at least for rank three. A further important class in the theory of hyperplane arrangements with particularly nice geometric, algebraic, topological, and combinatorial properties are the ...
Michael Cuntz
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On supersolvable and nearly supersolvable line arrangements [PDF]
Journal of Algebraic Combinatorics, 2018 v.3, a version of the Slope Problem, valid over the real and the complex numbers as well, is obtained, see Thm. 1.1 and Thm.
Gabriel Sticlaru +2 more
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Supersolvable restrictions of reflection arrangements
Journal of Combinatorial Theory - Series A, 2014 16 pages; final version, to appear in Journal of Combinatorial Theory, Series ...
Torsten Hoge, Gerhard Röhrle
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Supersolvable resolutions of line arrangements
Hokkaido Mathematical Journal, 2023 9 pages, 1 ...
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On complex supersolvable line arrangements
Journal of Algebra, 2020 v.9: Takuro Abe joins as a co-author, after proving that the conjectural upper bounds 3m-3 holds indeed.
Alexandru Dimca, Takuro Abe
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Real and complex supersolvable line arrangements in the projective plane [PDF]
Journal of Algebraic Combinatorics, 2020 17 pages; comments ...
Brian Harbourne +2 more
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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
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Simple Geometric Characterization of Supersolvable Arrangements
Rocky Mountain Journal of Mathematics, 2001 An arrangement of hyperplanes is a finite collection of \(\mathbb{C}\)-linear subspaces of dimension \(d-1\) in \(\mathbb{C}^d.\) Let \(A\) be an arrangement in \(\mathbb{C}^3\) and \(A^*\) be the natural projective arrangements in \(\mathbb{C}\mathbb{P}^2\) associated to it.
Jiang, Tan +2 more
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