Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4656710 | Journal of Combinatorial Theory, Series B | 2016 | 49 Pages |
Abstract
The present paper is concerned with the various algebraic structures supported by the set of Turán densities.We prove that the set of Turán densities of finite families of r -graphs is a non-trivial commutative semigroup, and as a consequence we construct explicit irrational densities for any r≥3r≥3. The proof relies on a technique recently developed by Pikhurko.We also show that the set of all Turán densities forms a graded ring, and from this we obtain a short proof of a theorem of Peng on jumps of hypergraphs.Finally, we prove that the set of Turán densities of families of r-graphs has positive Lebesgue measure if and only if it contains an open interval. This is a simple consequence of Steinhaus's theorem.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Codruţ Grosu,