MASCOTTE no longer exists => visit the new project-team
Seminaire MASCOTTEPoints covered by many simplices
par Daniel Kral
| Date : | 20/10/11 | | Time : | 11:00 | | Location : | Galois Coriolis |
Ă‚' Boros and Furedi (for d=2) and Barany (for arbitrary d) proved proved thatthere exists a constant c_d>0 such that for every set P of n points in R^din general position, there exists a point of R^d contained in at leastc_d [n choose d+1] (d+1)-simplices with vertices at the points of P.Gromov [Geom. Funct. Anal. 20 (2010), 416-526] improved the lower boundon c_d by topological means. Using methods from extremal combinatorics,we improve one of the quantities appearing in Gromov's approach andthereby provide a new stronger lower bound on c_d for arbitrary d.In particular, we improve the lower bound on c_3 from 0.06332 due toMatousek and Wagner to more than 0.07509 (the known upper bound on c_3is 0.09375).
This is a joint work with Lukas Mach and Jean-Sebastien Sereni
Page des séminaires
| 
