Results 21 to 30 of about 58 (48)
Supersolvable posets and fiber-type abelian arrangements
Selecta MathematicaAbstractWe 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.
Bibby, Christin, Delucchi, Emanuele
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The Orlik-Solomon algebra and the supersolvable class of arrangements
International Journal of Algebra, 2014 According to the powerful geometric properties of the hypersolvable order on the hyperplanes of a supersolvable arrangement, we introduced a sufficient condition on the Orlik-Solomon algebra for any central arrangement to have supersolvable analogue and we showed this condition as a necessary condition (not sufficient) on the Orlik-Solomon algebra for ...
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On an explicit correspondence between \(nbc\)-basis, chambers and minimal complex for real supersolvable arrangements [PDF]
Australas. J Comb., 2019 The authors give a very natural description of the bijections between the set of cells in the minimal CW-complex homotopy equivalent to the complement of a complexified real supersolvable arrangement $\mathcal{A}$, the \textbf{nbc}-basis (non broken circuit basis) of the Orlik-Solomon algebra associated to $\mathcal{A}$ and the set of chambers of ...
Settepanella, Simona, Torielli, Michele
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Combinatorial generation via permutation languages. VII. Supersolvable hyperplane arrangements
European Journal of CombinatoricsFor an arrangement $\mathcal{H}$ of hyperplanes in $\mathbb{R}^n$ through the origin, a region is a connected subset of $\mathbb{R}^n\setminus\mathcal{H}$. The graph of regions $G(\mathcal{H})$ has a vertex for every region, and an edge between any two vertices whose corresponding regions are separated by a single hyperplane from $\mathcal{H}$.
Sofia Brenner +4 more
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Hamiltonian Cycles in Simplicial and Supersolvable Hyperplane Arrangements
Motivated by the Gray code interpretation of Hamiltonian cycles in Cayley graphs, we investigate the existence of Hamiltonian cycles in tope graphs of hyperplane arrangements, with a focus on simplicial, reflection, and supersolvable arrangements. We confirm Hamiltonicity for all 3-dimensional simplicial arrangements listed in the Grünbaum--Cuntz ...
Körber, Veronika +3 more
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On an explicit correspondence between nbc-basis, chambers and minimal complex for real supersolvable arrangementsIn this paper we give a very natural description of the bijections between the set of cells in the minimal CW-complex homotopy equivalent to the complement of a complexified real supersolvable arrangement A, the nbc-basis of the Orlik-Solomon algebra associated to A and the set of chambers of A.
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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 ...
Gerhard Roehrle, Torsten Hoge
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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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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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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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