论文标题
HyperGraphTurán密度可以任意较大的代数学位
Hypergraph Turán densities can have arbitrarily large algebraic degree
论文作者
论文摘要
GROSU [关于Turán密度的代数和拓扑结构。 \ emph {j。组合。理论ser。 b} \ textbf {118}（2016）137--185]询问是否存在整数$ r \ ge 3 $和一个有限的$ r $ $ graphs家族，其turán密度为实际数字，具有（代数）程度（代数）学位（代数）大于$ r-1 $。在本说明中，我们表明，对于所有整数$ r \ ge 3 $和$ d $，都存在一个有限的$ r $ graphs家族，其turán密度至少具有〜$ d $，从而以强烈的形式回答了Grosu的问题。
Grosu [On the algebraic and topological structure of the set of Turán densities. \emph{J. Combin. Theory Ser. B} \textbf{118} (2016) 137--185] asked if there exist an integer $r\ge 3$ and a finite family of $r$-graphs whose Turán density, as a real number, has (algebraic) degree greater than~$r-1$. In this note we show that, for all integers $r\ge 3$ and $d$, there exists a finite family of $r$-graphs whose Turán density has degree at least~$d$, thus answering Grosu's question in a strong form.
