Bounds for Pach's Selection Theorem and for the Minimum Solid Angle in a Simplex

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10306823" target="_blank" >RIV/00216208:11320/15:10306823 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s00454-015-9720-z" target="_blank" >http://dx.doi.org/10.1007/s00454-015-9720-z</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00454-015-9720-z" target="_blank" >10.1007/s00454-015-9720-z</a>

Result language
angličtina
Original language name
Bounds for Pach's Selection Theorem and for the Minimum Solid Angle in a Simplex
Original language description
We give lower and upper bounds on the constant in Pach's selection theorem, which says that for every (d+1)-colored set of points in R^d, with n points of each color, one can select cn points from each color so that the intersection of all the rainbow simplices with vertices in the selected points is nonempty. In our construction for the upper bound, we use the fact that the minimum solid angle of every d-simplex is super-exponentially small. This fact was previously unknown and might be of independentinterest.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>
Continuities
S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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