Results 1 to 10 of about 1,232 (194)
k-Adjoint of hyperplane arrangements
Journal of Combinatorial Theory, Series AIn this paper, we introduce the $k$-adjoint of a given hyperplane arrangement $\mathcal{A}$ associated with rank-$k$ elements in the intersection lattice $L(\mathcal{A})$, which generalizes the classical adjoint proposed by Bixby and Coullard. The $k$-adjoint of $\mathcal{A}$ induces a decomposition of the Grassmannian, which we call the $\mathcal{A ...
Weikang Liang +2 more
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On free and plus-one generated curves arising from free curves by addition–deletion of a line
Bulletin of Mathematical SciencesIn a recent paper, after introducing the notion of plus-one generated hyperplane arrangements, Takuro Abe has shown that if we add (respectively, delete) a line to (respectively, from) a free line arrangement, then the resulting line arrangement is ...
Alexandru Dimca
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Jumping Numbers of Hyperplane Arrangements [PDF]
Communications in Algebra, 2010 M. Saito recently proved that the jumping numbers of a hyperplane arrangement depend only on the combinatorics of the arrangement. However, a formula in terms of the combinatorial data was still missing. In this note, we give a formula and a different proof of the fact that the jumping numbers of a hyperplane arrangement depend only on the ...
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The face lattice of hyperplane arrangements
Discrete Mathematics, 1988 A finite set \({\mathcal H}\) of hyperplanes in \({\mathbb{R}}^ d\) is called an arrangement. It determines a partition of \({\mathbb{R}}^ d\) into open topological cells, the face lattice \(L({\mathcal H})\) of which is studied by the author. He shows \(L({\mathcal H})\) to be shellable. To \({\mathcal H}\) there is assigned a zonotope \(\tilde Z\) in
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Electrical networks and hyperplane arrangements
Advances in Applied Mathematics, 2019 This paper studies \emph{Dirichlet arrangements}, a generalization of graphic hyperplane arrangements arising from electrical networks and order polytopes of finite posets. We generalize descriptions of combinatorial features of graphic arrangements to Dirichlet arrangements, including characteristic polynomials and supersolvability.
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The characteristic quasi-polynomials of hyperplane arrangements over residually finite Dedekind domains [PDF]
Enumerative Combinatorics and Applications, 2023 Masamichi Kuroda, Shuhei Tsujie
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Hyperplane arrangements: computations and conjectures
Advanced Studies in Pure Mathematics, 2019 This paper provides an overview of selected results and open problems in the theory of hyperplane arrangements, with an emphasis on computations and examples. We give an introduction to many of the essential tools used in the area, such as Koszul and Lie algebra methods, homological techniques, and the Bernstein-Gelfand-Gelfand correspondence, all ...
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Logarithmic Discriminants of Hyperplane Arrangements
Le Matematiche20 pages, comments welcome!
L. Kayser, A. Kretschmer, S. Telen
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Point Location in Arrangements of Hyperplanes
Information and Computation, 1993 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A Breast Cancer Image Classification Algorithm with 2c Multiclass Support Vector Machine. [PDF]
J Healthc Eng, 2023 Wajeed MA +6 more
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