Aaron Lin,Mehdi Makhul,Hossein Nassajian Mojarrad et al.
Aaron Lin et al.
An ordinary circle of a set P of n points in the plane is defined as a circle that contains exactly three points of P. We show that if P is not contained in a line or a circle, then P spans at least [Formula: see text] ordinary circles. Mor...
Wöden Kusner
Wöden Kusner
Using transversality and a dimension reduction argument, a result of Bezdek and Kuperberg is applied to polycylinders, showing that the optimal packing density of [Formula: see text] equals [Formula: see text] for all natural numbers n. ...
Ciprian Borcea,Ileana Streinu
Ciprian Borcea
We formulate and prove a periodic analog of Maxwell's theorem relating stressed planar frameworks and their liftings to polyhedral surfaces with spherical topology. We use our lifting theorem to prove deformation and rigidity-theoretic prop...
Tibor Jordán,Viktória E Kaszanitzky,Shin-Ichi Tanigawa
Tibor Jordán
We consider planar bar-and-joint frameworks with discrete point group symmetry in which the joint positions are as generic as possible subject to the symmetry constraint. We provide combinatorial characterizations for symmetry-forced rigidi...
Coloring [Formula: see text]-Embeddable [Formula: see text]-Uniform Hypergraphs [0.03%]
可嵌入k-均匀超图的着色问题公式上限公式观测公式 remarks公式 questions公式 conjectures公式
Carl Georg Heise,Konstantinos Panagiotou,Oleg Pikhurko et al.
Carl Georg Heise et al.
This paper extends the scenario of the Four Color Theorem in the following way. Let [Formula: see text] be the set of all [Formula: see text]-uniform hypergraphs that can be (linearly) embedded into [Formula: see text]. We investigate lower...
Leonidas J Guibas,Steve Y Oudot
Leonidas J Guibas
We present a novel reconstruction algorithm that, given an input point set sampled from an object S, builds a one-parameter family of complexes that approximate S at different scales. At a high level, our method is very similar in spirit to...