Paper Info

Title | ||
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On the algebraic and topological structure of the set of Turán densities. |

Abstract | ||
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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 |
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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 |

Authors (1 rows)

Cited by (1 rows)

References (18 rows)

Name | Order | Citations | PageRank |
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Codrut Grosu | 1 | 1 | 2.09 |