Extremal Configurations and Levels in Pseudoline Arrangements
نویسندگان
چکیده
منابع مشابه
Symmetric Simplicial Pseudoline Arrangements
A simplicial arrangement of pseudolines is a collection of topological lines in the projective plane where each region that is formed is triangular. This paper refines and develops David Eppstein’s notion of a kaleidoscope construction for symmetric pseudoline arrangements to construct and analyze several infinite families of simplicial pseudoline arrangements with high degrees of geometric sym...
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Introduction. A pseudoline is formed from a line by stretching the plane without tearing: it is the image of a line under a homeomorphism of the plane [13]. In arrangements of pseudolines, pairs of pseudolines intersect at most once and cross at their intersections. Pseudoline arrangements can be used to model sorting networks [1], tilings of convex polygons by rhombi [4], and graphs that have ...
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We study the set of all pseudoline arrangements with contact points which cover a given support. We define a natural notion of flip between these arrangements and study the graph of these flips. In particular, we provide an enumeration algorithm for arrangements with a given support, based on the properties of certain greedy pseudoline arrangements and on their connection with sorting networks....
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In [7] we have shown that special types of simplicial arrangements of d lines contain simple arrangements which are related to a class of bivariate polynomials Jd(x,y) having many critical points with few critical values. The polynomials have been used in the construction of algebraic surfaces with many A and D singularities [4, 5, 6, 7]. Tilings exhibiting non crystallographic symmetries have ...
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