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DCG
2016
3 years 1 months ago
Polynomial Partitioning on Varieties of Codimension Two and Point-Hypersurface Incidences in Four Dimensions
We present a polynomial partitioning theorem for finite sets of points in the real locus of a complex algebraic variety of codimension at most two. This result generalizes the pol...
Saugata Basu, Martín Sombra
DCG
2016
3 years 1 months ago
On the Odd Area of Planar Sets
The main result in the paper is a construction of a simple (in fact, just a union of two squares) set T in the plane with the following property. For every > 0 there if a famil...
Assaf Oren, Igor Pak, Rom Pinchasi
DCG
2016
3 years 1 months ago
Packing Convex Bodies by Cylinders
In [BL] in relation to the unsolved Bang’s plank problem (1951) we obtained a lower bound for the sum of relevant measures of cylinders covering a given d-dimensional convex bod...
Károly Bezdek, Alexander E. Litvak
DCG
2016
3 years 1 months ago
How to Walk Your Dog in the Mountains with No Magic Leash
Sariel Har-Peled, Amir Nayyeri, Mohammad R. Salava...
DCG
2016
3 years 1 months ago
Gap Probabilities and Betti Numbers of a Random Intersection of Quadrics
We consider the Betti numbers of an intersection of k random quadrics in RPn . Sampling the quadrics independently from the Kostlan ensemble, as n → ∞ we show that for each i ...
Antonio Lerario, Erik Lundberg
DCG
2016
3 years 1 months ago
On the Diameter of Lattice Polytopes
In this paper we show that the diameter of a d-dimensional lattice polytope in [0, k]n is at most k − 1 2 d . This result implies that the diameter of a d-dimensional half-integ...
Alberto Del Pia, Carla Michini
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