Add to ORKGWe consider sets L = {`1,..., `n} of n labeled lines in general position in R3, and study the order types of point sets {p1,..., pn} that stem from the intersections of the lines in L with (directed) planes Π, not parallel to any line of L, i.e., the proper cross-sections of L. As a main result we show that the number of different order types that can be obtained as cross-sections of L is O(n9), and that this bound is tight.
AbstractWe give a counterexample to a conjecture of G. Ringel on the order properties of a simple ar...
AbstractConsider all arrangements of lines in the plane with r distinct slopes. What is the smallest...
We prove geometric Ramsey-type statements on collections of lines in 3-space. These statements give ...
We consider sets L = {l1,...., ln} of n labeled lines in general position in R3, and study the order...
We consider sets L = {l(1),..., l(n)} of n labeled lines in general position in R-3, and study the o...
Given P and P', equally sized planar point sets in general position, we call a bijection from P to P...
We consider the following problem: Let L be an arrangement of n lines in R3 in general position colo...
Consider an ordered point set $P = (p_1,\ldots,p_n)$, its order type (denoted by $\chi_P$) is a map ...
AbstractWe extend the order type data base of all realizable order types in the plane to point sets ...
Given P and P\u27, equally sized planar point sets in general position, we call a bijection from P t...
We provide a complete data base of all realizable order types of 11 points in general position in th...
AbstractThere are several natural ways to extend the notion of the order of points on a line to high...
Given a real finite hyperplane arrangement A and a point p not on any of the hyperplanes, we define ...
We discuss certain open problems in the context of arrangements of lines in the plane. 1 Introduct i...
This paper begins by extending the notion of a combinatorial configuration of points and lines to a ...
AbstractWe give a counterexample to a conjecture of G. Ringel on the order properties of a simple ar...
AbstractConsider all arrangements of lines in the plane with r distinct slopes. What is the smallest...
We prove geometric Ramsey-type statements on collections of lines in 3-space. These statements give ...
We consider sets L = {l1,...., ln} of n labeled lines in general position in R3, and study the order...
We consider sets L = {l(1),..., l(n)} of n labeled lines in general position in R-3, and study the o...
Given P and P', equally sized planar point sets in general position, we call a bijection from P to P...
We consider the following problem: Let L be an arrangement of n lines in R3 in general position colo...
Consider an ordered point set $P = (p_1,\ldots,p_n)$, its order type (denoted by $\chi_P$) is a map ...
AbstractWe extend the order type data base of all realizable order types in the plane to point sets ...
Given P and P\u27, equally sized planar point sets in general position, we call a bijection from P t...
We provide a complete data base of all realizable order types of 11 points in general position in th...
AbstractThere are several natural ways to extend the notion of the order of points on a line to high...
Given a real finite hyperplane arrangement A and a point p not on any of the hyperplanes, we define ...
We discuss certain open problems in the context of arrangements of lines in the plane. 1 Introduct i...
This paper begins by extending the notion of a combinatorial configuration of points and lines to a ...
AbstractWe give a counterexample to a conjecture of G. Ringel on the order properties of a simple ar...
AbstractConsider all arrangements of lines in the plane with r distinct slopes. What is the smallest...
We prove geometric Ramsey-type statements on collections of lines in 3-space. These statements give ...