Results 11 to 20 of about 1,716 (199)
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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Affine and toric hyperplane arrangements [PDF]
Discrete & Computational Geometry, 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.
Margaret Readdy +5 more
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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 sigma-Grobner bases ...
Torielli, Michele, Palezzato, Elisa
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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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Depth in an Arrangement of Hyperplanes [PDF]
Discrete & Computational Geometry, 1999 A collection of \(n\) hyperplanes in \(\mathbb R^d\) forms a hyperplane arrangement. The depth of a point \(\theta\in\mathbb R^d\) is the smallest number of hyperplanes crossed by any ray emanating from \(\theta.\) The authors prove that for \(d = 2\) there always exists a point \(\theta\) with depth at least \(\lceil n/3\rceil.\) This theorem allows ...
Peter J. Rousseeuw, Mia Hubert
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IET Networks, EarlyView., 2022 Abstract Sensor technology advancements have provided a viable solution to fight COVID and to develop healthcare systems based on Internet of Things (IoTs). In this study, image processing and Artificial Intelligence (AI) are used to improve the IoT framework.
Noor M Allayla +2 more
wiley +1 more source
The freeness of Ish arrangements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 The Ish arrangement was introduced by Armstrong to give a new interpretation of the $q; t$-Catalan numbers of Garsia and Haiman. Armstrong and Rhoades showed that there are some striking similarities between the Shi arrangement and the Ish arrangement ...
Takuro Abe +2 more
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Gallery Posets of Supersolvable Arrangements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We introduce a poset structure on the reduced galleries in a supersolvable arrangement of hyperplanes. In particular, for Coxeter groups of type A or B, we construct a poset of reduced words for the longest element whose Hasse diagram is the graph of ...
Thomas McConville
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From Bruhat intervals to intersection lattices and a conjecture of Postnikov [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We prove the conjecture of A. Postnikov that ($\mathrm{A}$) the number of regions in the inversion hyperplane arrangement associated with a permutation $w \in \mathfrak{S}_n$ is at most the number of elements below $w$ in the Bruhat order, and ($\mathrm ...
Axel Hultman +3 more
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