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Generic section of a hyperplane arrangement and twisted Hurewicz maps
Topology and Its Applications, 2008 We consider a twisted version of the Hurewicz map on the complement of a hyperplane arrangement. The purpose of this paper is to prove surjectivity of the twisted Hurewicz map under some genericity conditions. As a corollary, we also prove that a generic
Masahiko Yoshinaga
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Hyperplane arrangements between Shi and Ish [PDF]
Electronic Notes in Discrete Mathematics, 2018 We introduce a new family of hyperplane arrangements in dimension n≥3 that includes both the Shi arrangement and the Ish arrangement. We prove that all the members of this family have the same number of regions -- the connected components of the ...
Rui Duarte, Antonio Guedes De Oliveira
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Lattice and order properties of the poset of regions in a hyperplane arrangement [PDF]
Algebra Universalis, 2003 We show that the poset of regions (with respect to a canonical base region)of a supersolvable hyperplane arrangement is a congruence normal lattice. Specifically,the poset of regions of a supersolvable arrangement of rank k is obtained via a sequenceof ...
Nathan Reading, Reading Nathan
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Computing Characteristic Polynomials of Hyperplane Arrangements with Symmetries
Discrete and Computational Geometry, 2023 Brysiewicz T, Eble H, Kühne L. Computing characteristic polynomials of hyperplane arrangements with symmetries. Discrete and Computational Geometry. 2023;70:1356–1377.We introduce a new algorithm computing the characteristic polynomials of hyperplane ...
Taylor Brysiewicz, Lukas Kühne
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The Varchenko determinant of an oriented matroid [PDF]
Transactions on Combinatorics, 2021 Varchenko introduced in 1993 a distance function on the chambers of a hyperplane arrangement that gave rise to a determinant whose entry in position $(C, D)$ is the distance between the chambers $C$ and $D$, and computed that determinant. In 2017, Aguiar
Hery Randriamaro
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Hyperfactord of Shi arrangement Sh(A2) and Sh(A3)
Al-Mustansiriyah Journal of Science, 2022 In this paper, we introduce the region and the faces poset of shi arrangement that J. Y. Shi firstly introduced it. This is an affine arrangement, each of whose hyperplane is parallel to some"hyperplane of Coxeter arrangement"(Braid arrangement), the ...
Alaa A. A. Al-Mujmaey +1 more
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Counting Shi regions with a fixed separating wall [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 Athanasiadis introduced separating walls for a region in the extended Shi arrangement and used them to generalize the Narayana numbers. In this paper, we fix a hyperplane in the extended Shi arrangement for type A and calculate the number of dominant ...
Susanna Fishel +2 more
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Affine and toric arrangements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We extend the Billera―Ehrenborg―Readdy map between the intersection lattice and face lattice of a central hyperplane arrangement to affine and toric hyperplane arrangements.
Richard Ehrenborg +2 more
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The arithmetic Tutte polynomials of the classical root systems [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 Many combinatorial and topological invariants of a hyperplane arrangement can be computed in terms of its Tutte polynomial. Similarly, many invariants of a hypertoric arrangement can be computed in terms of its arithmetic Tutte polynomial. We compute the
Federico Ardila +2 more
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Wonderful compactifications and rational curves with cyclic action
Forum of Mathematics, Sigma, 2023 We prove that the moduli space of rational curves with cyclic action, constructed in our previous work, is realizable as a wonderful compactification of the complement of a hyperplane arrangement in a product of projective spaces.
Emily Clader +3 more
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