Results 91 to 100 of about 1,230 (193)
Computing the Tutte Polynomial of hyperplane arrangements [PDF]
, 2009 textWe are studying the Tutte Polynomial of hyperplane arrangements. We discuss some previous work done to compute these polynomials. Then we explain our method to calculate the Tutte Polynomial of some arrangements more efficiently.
Geldon, Todd Wolman
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The facial weak order on hyperplane arrangements
, 2022 34 pages, 12 figuresInternational audienceWe extend the facial weak order from finite Coxeter groups to central hyperplane arrangements. The facial weak order extends the poset of regions of a hyperplane arrangement to all its faces.
Hohlweg, Christophe +3 more
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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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Computing Characteristic Polynomials of Hyperplane Arrangements with Symmetries
We introduce a new algorithm computing the characteristic polynomials of hyperplane arrangements which exploits their underlying symmetry groups.
Kühne, Lukas +2 more
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Hyperplane Arrangements with Large Average Diameter [PDF]
, 2007 This thesis deals with combinatorial properties of hyperplane arrangements. In particular, we address a conjecture of Deza, Terlaky and Zinchenko stating that the largest possible average diameter of a bounded cell of a simple hyperplane arrangement is ...
Xie, Feng
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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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Birational Geometry of Matroids and Abstract Hyperplane Arrangements
, 2023 A matroid is a machine capturing linearity of mathematical objects and producing combinatorial structures. Matroid structure arises everywhere since linearity is a ubiquitous concept.
Shin, Jaeho
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Logarithmic Discriminants of Hyperplane Arrangements
Le Matematiche20 pages, comments welcome!
L. Kayser, A. Kretschmer, S. Telen
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