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On possible Turan densities
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Pikhurko, Oleg (2014) On possible Turan densities. Israel Journal of Mathematics . doi:10.1007/s11856-014-0031-5
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Official URL: http://dx.doi.org/10.1007/s11856-014-0031-5
Abstract
The Tur\'an density \pi(H) of a family H of k-graphs is the limit as n tends to infinity of the maximum edge density of an H-free k-graph on n vertices. Let I^k consist of all possible Tur\'an densities and let F^k be the set of Tur\'an densities of finite k-graph families.
Here we prove that F^k contains every density obtained from an arbitrary finite construction by optimally blowing it up and using recursion inside the specified set of parts. As an application, we show that F^k contains an irrational number for each k\ge 3.
Also, we show that I^k has cardinality of the continuum. In particular, I^k is not equal to F^k.
| Item Type: | Submitted Journal Article | ||||
|---|---|---|---|---|---|
| Divisions: | Faculty of Science > Mathematics | ||||
| Journal or Publication Title: | Israel Journal of Mathematics | ||||
| Publisher: | Magnes Press | ||||
| ISSN: | 0021-2172 | ||||
| Official Date: | 14 February 2014 | ||||
| Dates: |
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| DOI: | 10.1007/s11856-014-0031-5 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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