Name
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 ¿ 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. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1016/j.jctb.2016.01.001 | J. Comb. Theory, Ser. B |
Keywords | Field | DocType |
Turán densities,Uniform hypergraphs,Jumps | Discrete mathematics,Algebraic number,Commutative property,Graded ring,Algebraic structure,Lebesgue measure,Irrational number,If and only if,Semigroup,Mathematics | Journal |
Volume | Issue | ISSN |
118 | C | 0095-8956 |
Citations | PageRank | References |
1 | 0.40 | 18 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Codrut Grosu | 1 | 1 | 2.09 |