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Polynomial estimates towards a sharp Helly-type theorem for convex sets
| Content Provider | Semantic Scholar |
|---|---|
| Author | Brazitikos, Silouanos |
| Copyright Year | 2017 |
| Abstract | We discuss a problem posed by Bárány, Katchalski and Pach: if {Pi : i ∈ I} is a family of closed convex sets in R such that diam (⋂ i∈I Pi ) = 1 then there exist s 6 2n and i1, . . . , is ∈ I such that diam (Pi1 ∩ · · · ∩ Pis) 6 Cn, where Cn 6 c √ n for an absolute constant c > 0. We prove that this statement holds true with Cn 6 cn. All the previously known estimates for Cn were exponential or superexponential in the dimension n. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://users.uoa.gr/~apgiannop/polynomial-helly.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
