Results 11 to 20 of about 1,721 (200)
Affine and Toric Hyperplane Arrangements [PDF]
Discrete & Computational Geometry, 2009 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. For arrangements on the torus, we also generalize Zaslavsky's fundamental results on the number of regions.
Richard Ehrenborg +2 more
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Hyperplane Arrangements and Diagonal Harmonics [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 In 2003, Haglund's bounce statistic gave the first combinatorial interpretation of the q,t-Catalan numbers and the Hilbert series of diagonal harmonics. In this paper we propose a new combinatorial interpretation in terms of the affine Weyl group of type
Drew Armstrong
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Combinatorially equivalent hyperplane arrangements [PDF]
Advances in Applied Mathematics, 2021 We study the combinatorics of hyperplane arrangements over arbitrary fields. Specifically, we determine in which situation an arrangement and its reduction modulo a prime number have isomorphic lattices via the use of minimal strong $σ$-Gröbner bases.
Elisa Palezzato, Michele Torielli
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Projection Volumes of Hyperplane Arrangements [PDF]
Discrete and Computational Geometry, 2011 We prove that for any finite real hyperplane arrangement the average projection volumes of the maximal cones is given by the coefficients of the characteristic polynomial of the arrangement. This settles the conjecture of Drton and Klivans that this held for all finite real reflection arrangements. The methods used are geometric and combinatorial. As a
Caroline J Klivans, Ed Swartz
exaly +4 more sources
Deformations of Coxeter Hyperplane Arrangements
Journal of Combinatorial Theory - Series A, 2000 33 ...
Richard P Stanley, Alexander Postnikov
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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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More Bisections by Hyperplane Arrangements [PDF]
Discrete & Computational Geometry, 2021 A union of an arrangement of affine hyperplanes $H$ in $R^d$ is the real algebraic variety associated to the principal ideal generated by the polynomial $p_{H}$ given as the product of the degree one polynomials which define the hyperplanes of the arrangement.
Pavle V. M. Blagojevic +3 more
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Hyperplane Arrangements in polymake [PDF]
, 2020 Hyperplane arrangements form the latest addition to the zoo of combinatorial objects dealt with by polymake. We report on their implementation and on a algorithm to compute the associated cell decomposition. The implemented algorithm performs significantly better than brute force alternatives, as it requires less convex hulls computations.
Lars Kastner, Marta Panizzut
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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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