Results 1 to 10 of about 40 (40)
Ramsey-type theorems for lines in 3-space [PDF]
Discrete Mathematics & Theoretical Computer Science, 2016 We prove geometric Ramsey-type statements on collections of lines in 3-space. These statements give guarantees on the size of a clique or an independent set in (hyper)graphs induced by incidence relations between lines, points, and reguli in 3-space ...
Jean Cardinal +2 more
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Equivariant perverse sheaves on Coxeter arrangements and buildings [PDF]
Épijournal de Géométrie Algébrique, 2019 When $W$ is a finite Coxeter group acting by its reflection representation on $E$, we describe the category ${\mathsf{Perv}}_W(E_{\mathbb C}, {\mathcal{H}}_{\mathbb C})$ of $W$-equivariant perverse sheaves on $E_{\mathbb C}$, smooth with respect to the ...
Martin H. Weissman
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Triangular arrangements on the projective plane [PDF]
Épijournal de Géométrie Algébrique, 2023 In this work we study line arrangements consisting in lines passing through three non-aligned points. We call them triangular arrangements. We prove that any combinatorics of a triangular arrangement is always realized by a Roots-of-Unity-Arrangement ...
Simone Marchesi, Jean Vallès
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Supersolvable orders and inductively free arrangements
Open Mathematics, 2017 In this paper, we define the supersolvable order of hyperplanes in a supersolvable arrangement, and obtain a class of inductively free arrangements according to this order.
Gao Ruimei, Cui Xiupeng, Li Zhe
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A NOTE ON RICH LINES IN TRULY HIGH DIMENSIONAL SETS
Forum of Mathematics, Sigma, 2016 We modify an argument of Hablicsek and Scherr to show that if a collection of points in $\mathbb{C}^{d}$ spans many
JOSHUA ZAHL
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On the freeness of hypersurface arrangements consisting of hyperplanes and spheres
Open Mathematics, 2018 Let V be a smooth variety. A hypersurface arrangement 𝓜 in V is a union of smooth hypersurfaces, which locally looks like a union of hyperplanes. We say 𝓜 is free if all these local models can be chosen to be free hyperplane arrangements.
Gao Ruimei, Dai Qun, Li Zhe
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SYLVESTER–GALLAI TYPE THEOREMS FOR APPROXIMATE COLLINEARITY
Forum of Mathematics, Sigma, 2014 We study questions in incidence geometry where the precise position of points is ‘blurry’ (for example due to noise, inaccuracy or error). Thus lines are replaced by narrow tubes, and more generally affine subspaces are replaced by their small ...
ALBERT AI +3 more
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IMPROVED RANK BOUNDS FOR DESIGN MATRICES AND A NEW PROOF OF KELLY’S THEOREM
Forum of Mathematics, Sigma, 2014 We study the rank of complex sparse matrices in which the supports of different columns have small intersections. The rank of these matrices, called design matrices, was the focus of a recent work by Barak et al.
ZEEV DVIR +2 more
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CUTTING A PART FROM MANY MEASURES
Forum of Mathematics, Sigma, 2019 Holmsen, Kynčl and Valculescu recently conjectured that if a finite set $X$ with $\ell n$ points in $\mathbb{R}^{d}$ that is colored by $m$ different colors can be partitioned into $n$ subsets of $\ell$ points each, such that each subset contains points ...
PAVLE V. M. BLAGOJEVIĆ +3 more
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Morphisms and Order Ideals of Toric Posets
Mathematics, 2016 Toric posets are in some sense a natural “cyclic” version of finite posets in that they capture the fundamental features of a partial order but without the notion of minimal or maximal elements.
Matthew Macauley
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