Geodesic
A slight improvement to the colored Bárány's theorem
Zilin Jiang1
1Carnegie Mellon University
The electronic journal of combinatorics, Tome 21 (2014) no. 4
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Suppose $d+1$ absolute continuous probability measures $m_0, \ldots, m_d$ on $\mathbb{R}^d$ are given. In this paper, we prove that there exists a point of $\mathbb{R}^d$ that belongs to the convex hull of $d+1$ points $v_0, \ldots, v_d$ with probability at least $\frac{2d}{(d+1)!(d+1)}$, where each point $v_i$ is sampled independently according to probability measure $m_i$.
DOI : 10.37236/4374
Classification : 05B25, 60C99
Mots-clés : discrete geometry, point selection problem, topological methods in combinatorics

Zilin Jiang  1

1 Carnegie Mellon University 
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     title = {A slight improvement to the colored {B\'ar\'any's} theorem},
     journal = {The electronic journal of combinatorics},
     year = {2014},
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     doi = {10.37236/4374},
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Zilin Jiang. A slight improvement to the colored Bárány's theorem. The electronic journal of combinatorics, Tome 21 (2014) no. 4. doi: 10.37236/4374

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