Results 31 to 40 of about 58 (47)

The $\textbf{nbc}$ minimal complex of supersolvable arrangements

, 2015
In this paper we give a very natural description of the bijections between the minimal CW-complex homotopy equivalent to the complement of a supersolvable arrangement $\mathcal{A}$, the $\textbf{nbc}$ basis of the Orlik-Solomon algebra associated to $\mathcal{A}$ and the set of chambers of $\mathcal{A}$.
Settepanella, Simona, Torielli, Michele
openaire   +2 more sources

Monodromy of supersolvable toric arrangements

We study topological aspects of supersolvable abelian arrangements, toric arrangements in particular. The complement of such an arrangement sits atop a tower of fiber bundles, and we investigate the relationship between these bundles and bundles involving classical configuration spaces.
Bibby, Christin, Cohen, Daniel C., Delucchi, Emanuele   +2 more
openaire   +2 more sources

Supersolvable posets and fiber-type abelian arrangements

Selecta Mathematica
AbstractWe 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
openaire   +3 more sources

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 ...
openaire   +1 more source

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
openaire   +1 more source

Combinatorial generation via permutation languages. VII. Supersolvable hyperplane arrangements

European Journal of Combinatorics
For 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, Jean Cardinal, Thomas McConville, Arturo Merino, Torsten Mütze   +4 more
openaire   +3 more sources

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, Schnieders, Tobias, Stricker, Jan, Walizadeh, Jasmin   +3 more
openaire   +2 more sources

On an explicit correspondence between nbc-basis, chambers and minimal complex for real supersolvable arrangements

On an explicit correspondence between nbc-basis, chambers and minimal complex for real supersolvable arrangements
In 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.
openaire  

Supersolvability of complementary signed-graphic hyperplane arrangements [PDF]

Australas. J Comb., 2004
The 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
openaire   +1 more source

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Finite Factorizable Groups with $$\mathbb P$$-Subnormal $$\mathrm v$$-Supersolvable and $$\mathrm{sh}$$-Supersolvable Factors

Mathematical Notes, 2022
Monakhov V S, V S Monakhov
exaly