论文标题
Quasirandom强迫周期的方向
Quasirandom forcing orientations of cycles
论文作者
论文摘要
如果限制（同构）密度为$ h $，则在一系列锦标赛中的限制密度为$ 2^{ - \ | h \ |} $，并且仅当序列是quasirandom时，则面向$ h $是quasirandom-forcing。我们研究以下结果的概括：当且仅当$ \ ell \ equiv 2 $ mod $ 4 $时，当时$ \ ell $的周期的环状方向是quasirandom-forcing。 我们表明，奇数周期没有方向是quasirandom for的。在偶数循环的情况下，我们在方向上找到了足够的条件，可以通过识别必要的条件来补充。使用我们用于获取它们的一般结果和光谱技术，我们将长度高达$ 10 $的周期的方向分类为quasirandom-forning。
An oriented graph $H$ is quasirandom-forcing if the limit (homomorphism) density of $H$ in a sequence of tournaments is $2^{-\|H\|}$ if and only if the sequence is quasirandom. We study generalizations of the following result: the cyclic orientation of a cycle of length $\ell$ is quasirandom-forcing if and only if $\ell\equiv 2$ mod $4$. We show that no orientation of an odd cycle is quasirandom-forcing. In the case of even cycles, we find sufficient conditions on an orientation to be quasirandom-forcing, which we complement by identifying necessary conditions. Using our general results and spectral techniques used to obtain them, we classify which orientations of cycles of length up to $10$ are quasirandom-forcing.
