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Tangencies between families of disjoint regions in the plane

Publications associées (45)

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Distinct distances between points and lines

Frank de Zeeuw, Adrian Claudiu Valculescu, Shakhar Smorodinsky

We show that for m points and n lines in R-2, the number of distinct distances between the points and the lines is Omega(m(1/5)n(3/5)), as long as m(1/2)

Elsevier Science Bv2018

Computing Crowd Consensus with Partial Agreement (Extended Abstract)

Quoc Viet Hung Nguyen, Thành Tâm Nguyên

Crowdsourcing has been widely established as a means to enable human computation at large-scale, in particular for tasks that require manual labelling of large sets of data items. Answers obtained from heterogeneous crowd workers are aggregated to obtain a ...

IEEE2018

Computing Crowd Consensus with Partial Agreement

Quoc Viet Hung Nguyen, Thành Tâm Nguyên

2018

On some algebraic and extremal problems in discrete geometry

Seyed Hossein Nassajianmojarrad

In the present thesis, we delve into different extremal and algebraic problems arising from combinatorial geometry. Specifically, we consider the following problems. For any integer

n\ge 3

, we define

e(n)

to be the minimum positive integer such that an ...

EPFL2017

An improvement on the number of simplices in F-q(d)

Van Thang Pham

Let epsilon be a set of points in F-q(d). Bennett et al. (2016) proved that if \epsilon\ >> [GRAHICS] then epsilon determines a positive proportion of all k-simplices. In this paper, we give an improvement of this result in the case when epsilon is the Car ...

Elsevier Science Bv2017

For integers n >= s >= 2 let e (n, s) denote the maximum of vertical bar F vertical bar, where F is a family of subsets of an n- element set and F contains no s pairwise disjoint members. Half a century ago, solving a conjecture of Erd. os, Kleitman determ ...

Wiley2017

Essential connectedness and the rigidity problem for Gaussian symmetrization

Maria Colombo

We provide a geometric characterization of rigidity of equality cases in Ehrhard ' s symmetrization inequality for Gaussian perimeter. This condition is formulated in terms of a new measure-theoretic notion of connectedness for Borel sets, inspired by Fede ...

2017

In this Comment I challenge the main conclusions of Ref. [1]. The main reason for this Comment is the large number of questions on the details of the experiment that led me to request the raw data. I have obtained two sets of raw data. After a long discuss ...

American Physical Society2016

Suppose k is a positive integer and X is a k-fold packing of the plane by infinitely many arc-connected compact sets, which means that every point of the plane belongs to at most k sets. Suppose there is a function f(n) = o(n(2)) with the property that any ...

Cambridge Univ Press2016

Unsplittable Coverings in the Plane

János Pach

A system of sets forms an m-fold covering of a set X if every point of X belongs to at least m of its members. A 1-fold covering is called a covering. The problem of splitting multiple coverings into several coverings was motivated by classical density est ...

Springer-Verlag Berlin2016