Results 21 to 30 of about 57 (42)
Inductive and divisional posets
Journal of the London Mathematical Society, Volume 109, Issue 1, January 2024.Abstract We call a poset factorable if its characteristic polynomial has all positive integer roots. Inspired by inductive and divisional freeness of a central hyperplane arrangement, we introduce and study the notion of inductive posets and their superclass of divisional posets.
Roberto Pagaria +3 more
wiley +1 more source
Supersolvability and the Koszul property of root ideal arrangements [PDF]
Proceedings of the American Mathematical Society, 2015 13 pages, 3 ...
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Koszulness and supersolvability for Dirichlet arrangements
Proceedings of the American Mathematical Society, 2019 We prove that the cone over a Dirichlet arrangement is supersolvable if and only if its Orlik-Solomon algebra is Koszul. This was previously shown for four other classes of arrangements. We exhibit an infinite family of cones over Dirichlet arrangements that are combinatorially distinct from these other four classes.
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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
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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 +2 more
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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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