منابع مشابه
Lines in Higgledy-Piggledy Arrangement
In this article, we examine sets of lines in PG(d,F) meeting each hyperplane in a generator set of points. We prove that such a set has to contain at least b1.5dc lines if the field F has at least b1.5dc elements, and at least 2d− 1 lines if the field F is algebraically closed. We show that suitable 2d − 1 lines constitute such a set (if |F| > 2d − 1), proving that the lower bound is tight over...
متن کاملLines in higgledy-piggledy position
In this article, we examine sets of lines in PG(d,F) meeting each hyperplane in a generator set of points. We prove that such a set has to contain at least 1.5d lines if the field F has more than 1.5d elements, and at least 2d− 1 lines if the field F is algebraically closed. We show that suitable 2d−1 lines constitute such a set (if |F| ≥ 2d−1), proving that the lower bound is tight over algebr...
متن کاملWeighted Region Problem in Arrangement of Lines
In this paper, a geometric shortest path problem in weighted regions is discussed. An arrangement of lines A, a source s, and a target t are given. The objective is to find a weighted shortest path, πst, from s to t. Existing approximation algorithms for weighted shortest paths work within bounded regions (typically triangulated). To apply these algorithms to unbounded regions, such as arrangem...
متن کاملUnbounded Regions in an Arrangement of Lines in the Plane
We take a set Ω of n points and an arrangement Σ of m lines in the plane which avoid these points but separate any two of them. We suppose these satisfy the following unboundedness property: for each point x ∈ Ω there is a homotopy from Σ to Σ′ avoiding Ω so that x is in an unbounded component of the complement of Σ′. It is proved that then n ≤ 2m. This result is required to partially solve a p...
متن کاملCrossing by lines all edges of a line arrangement
Let L be a family of n blue lines in the real projective plane. Suppose that R is a collection of m red lines, different from the blue lines, and it is known that every edge in the arrangement A(L) is crosses by a line in R. We show that m ≥ n−1 3.5 . Our result is more general and applies to pseudo-line arrangements A(L), and even weaker assumptions are required for R.
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2014
ISSN: 1077-8926
DOI: 10.37236/4149