121
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DCG
2016
10 years 18 days ago
2016
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...
139
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DCG
2016
10 years 18 days ago
2016
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...
209
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DCG
2016
10 years 18 days ago
2016
128
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DCG
2016
10 years 18 days ago
2016
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...
121
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DCG
2016
10 years 18 days ago
2016
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 ...
133
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DCG
2016
10 years 18 days ago
2016
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...