论文标题
Turán数字和切换
Turán numbers and switching
论文作者
论文摘要
使用锦标赛上的开关操作，我们在$ r $ r $ r+1 $的顶点的Turán数字上获得了一些新的下限，并带有3美元的边缘。对于$ r = 4 $，在以前的工作中使用Paley锦标赛构建了极端示例。我们表明，使用傅立叶分析，这些示例是独一无二的（在特定意义上）。 $ 3 $ - 锦标赛是由顶点集合中不同顶点的交替功能给出的“高级”版本的“高级”版本。我们表明，$ 3 $ tournaments也可以享受开关操作，并使用它来为切换类的大小提供水平排列的大小，从而概括了Babai-Cameron的结果。
Using a switching operation on tournaments we obtain some new lower bounds on the Turán number of the $r$-graph on $r+1$ vertices with $3$ edges. For $r=4$, extremal examples were constructed using Paley tournaments in previous work. We show that these examples are unique (in a particular sense) using Fourier analysis. A $3$-tournament is a `higher order' version of a tournament given by an alternating function on triples of distinct vertices in a vertex set. We show that $3$-tournaments also enjoy a switching operation and use this to give a formula for the size of a switching class in terms of level permutations, generalising a result of Babai--Cameron.
