Results 21 to 30 of about 1,721 (200)
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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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 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
doaj +1 more source
Hyperplane Arrangements over the Ring of Integers Modulo N. [PDF]
, 2023 Let V be a finite vector space of dimension n over the field K. A hyperplane in V is an n − 1 dimensional subspace of V defined by an equation of the form∑ni=1 aixi = 0, ai ∈ K, (x1, ..., xn) ∈ V .
Obeahon, Ehiareshan James
core +2 more sources
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
doaj +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
doaj +1 more source
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
doaj +1 more source
Cell Complexities in Hyperplane Arrangements [PDF]
Discrete and Computational Geometry, 2004 The complexity of some cells of an hyperplane arrangement in \(R^d\) is the total number of faces of all dimensions of these cells. The authors show that the complexity of \(m\) distinct cells in an arrangement of \(n\) hyperplanes in dimension \(d\geq 4\) is \(O(m^{1/2}n^{d/2}\log^{(\lfloor d/2\rfloor-2)}n)\).
Boris Aronov, Micha Sharir
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