منابع مشابه
Convex Quadrilaterals and k-Sets
We prove that the minimum number of convex quadrilaterals determined by n points in general position in the plane – or in other words, the rectilinear crossing number of the complete graph Kn – is at least ( 38 + 10 −5) ( n 4 ) +O(n). Our main tool is a lower bound on the number of (≤ k)-sets of the point set: we show that for every k ≤ n/2, there are at least 3 ( k+1 2 ) subsets of size at mos...
متن کاملToric Geometry of Convex Quadrilaterals
We provide an explicit resolution of the Abreu equation on convex labeled quadrilaterals. This confirms a conjecture of Donaldson in this particular case and implies a complete classification of the explicit toric Kähler– Einstein and toric Sasaki–Einstein metrics constructed in [6, 23, 14]. As a byproduct, we obtain a wealth of extremal toric (complex) orbi-surfaces, including Kähler–Einstein ...
متن کاملMeshing of Hexagons into Convex Quadrilaterals
Efficient electromagnetic analysis of the composite metallic and dielectric structures in the frequency domain based on the Method of Moments applied to the Surface Integral Equations is provided, if building blocks have the form of bilinear surfaces (in particular, flat quads), and if analysis is supported by the higher order basis functions. Heterogenous surfaces of many 3D structures can be ...
متن کاملCovering the Convex Quadrilaterals of Point Sets
For a point set P on the plane, a four element subset S ⊂ P is called a 4-hole of P if the convex hull of S is a quadrilateral and contains no point of P in its interior. Let R be a point set on the plane. We say that a point set B covers all the 4-holes of R if any 4-hole of R contains an element of B in its interior. We show that if |R| ≥ 2|B|+5 then B cannot cover all the 4-holes of R. A sim...
متن کاملAcute Triangulations of Doubly Covered Convex Quadrilaterals
Motivated by various applications triangulations of surfaces using only acute triangles have been recently studied. Triangles and quadrilaterals can be triangulated with at most 7, respectively 10, acute triangles. Doubly covered triangles can be triangulated with at most 12 acute triangles. In this paper we investigate the acute triangulations of doubly covered convex quadrilaterals, and show ...
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ژورنال
عنوان ژورنال: Missouri Journal of Mathematical Sciences
سال: 1994
ISSN: 0899-6180
DOI: 10.35834/1994/0601010