AbstractLet L = {l1, …, ln} be a collection of n lines in three-dimensional space. A joint of L is a point incident to three noncoplanar lines of L. We prove that the number of joints of L is O(n2314log3114 n), which is O(n1.643). This improves a previous bound of O(n74) due to Chazelle et al. The proof makes use of recent range searching techniques and of a structural analysis of the pattern of intersections between n lines in space
AbstractLet P be a set of n points in R3, not all of which are in a plane and no three on a line. We...
For an arrangement of $n$ lines in the real projective plane, we denote by $f$ the number of regions...
Arrangements of lines and pseudolines are important and appealing objects for research in discrete a...
Let L be a set of n lines in space. A joint of L is a point in R 3 where at least three non-coplanar...
AbstractWe extend (and somewhat simplify) the algebraic proof technique of Guth and Katz (2010) [9],...
A joint of a set of lines $\mathcal{L}$ in $\mathbb{F}^d$ is a point that is contained in $d$ lines ...
We prove that in a simple matroid, the maximal number of joints formed by L lines is o(L[superscript...
Abstract We generalize the Guth–Katz joints theorem from lines to varieties. A special ...
Two- and three-dimensional rectangular dissections are considered as sets of intersecting line and p...
We generalize the Guth--Katz joints theorem from lines to varieties. A special case says that $N$ pl...
Let \(\mathcal{L}\) be a family of lines and let \(\mathcal{P}\) be a family of \(k\)-planes in \(\...
This thesis investigates two problems that are discrete analogues of two harmonic analytic problems...
Consider a finite set of lines in 3-space. A joint is a point where three of these lines (not lying ...
We advance the study of collections of open linkages in 3-space that may be interlocked in the sense...
Let P be a set of n points in R 3, not all of which are in a plane and no three on a line. We partia...
AbstractLet P be a set of n points in R3, not all of which are in a plane and no three on a line. We...
For an arrangement of $n$ lines in the real projective plane, we denote by $f$ the number of regions...
Arrangements of lines and pseudolines are important and appealing objects for research in discrete a...
Let L be a set of n lines in space. A joint of L is a point in R 3 where at least three non-coplanar...
AbstractWe extend (and somewhat simplify) the algebraic proof technique of Guth and Katz (2010) [9],...
A joint of a set of lines $\mathcal{L}$ in $\mathbb{F}^d$ is a point that is contained in $d$ lines ...
We prove that in a simple matroid, the maximal number of joints formed by L lines is o(L[superscript...
Abstract We generalize the Guth–Katz joints theorem from lines to varieties. A special ...
Two- and three-dimensional rectangular dissections are considered as sets of intersecting line and p...
We generalize the Guth--Katz joints theorem from lines to varieties. A special case says that $N$ pl...
Let \(\mathcal{L}\) be a family of lines and let \(\mathcal{P}\) be a family of \(k\)-planes in \(\...
This thesis investigates two problems that are discrete analogues of two harmonic analytic problems...
Consider a finite set of lines in 3-space. A joint is a point where three of these lines (not lying ...
We advance the study of collections of open linkages in 3-space that may be interlocked in the sense...
Let P be a set of n points in R 3, not all of which are in a plane and no three on a line. We partia...
AbstractLet P be a set of n points in R3, not all of which are in a plane and no three on a line. We...
For an arrangement of $n$ lines in the real projective plane, we denote by $f$ the number of regions...
Arrangements of lines and pseudolines are important and appealing objects for research in discrete a...
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