论文标题
HyperCube的诱导性
Inducibility in the hypercube
论文作者
论文摘要
令$ q_d $为尺寸$ d $的超双立方体，让$ h $和$ k $为顶点套装$ v（q_d）$的子集，称为$ q_d $中的配置。我们说，如果有$ q_d $的自动形态，将$ h $发送到$ k $，则$ k $是$ h $的\ emph {确切复制}。令$ n \ geq d $为整数，让$ h $为$ q_d $中的配置，让$ s $为$ q_n $中的配置。我们让$λ（h，d，n）$是最大的，与所有配置相比，$ q_n $中的所有配置$ s $，属于$ s $ d $ -d $ r $ $ q_n $的一小部分，其中$ s \ cap r $是$ h $的精确副本，我们定义了$ d $ d $ d $ d $ d $ $ nigen $ nigen $ nind $ nigne $ nimity $ nimity $ nigens $ nigen of younge n y y y n y n y y y y n y n y Infe $λ（h，d，n）$。我们确定$λ（h，d）$的$ q_3 $和$ q_4 $的几种配置以及无限的配置家族。与图的诱导性有很强的联系。
Let $Q_d$ be the hypercube of dimension $d$ and let $H$ and $K$ be subsets of the vertex set $V(Q_d)$, called configurations in $Q_d$. We say that $K$ is an \emph{exact copy} of $H$ if there is an automorphism of $Q_d$ which sends $H$ onto $K$. Let $n\geq d$ be an integer, let $H$ be a configuration in $Q_d$ and let $S$ be a configuration in $Q_n$. We let $λ(H,d,n)$ be the maximum, over all configurations $S$ in $Q_n$, of the fraction of sub-$d$-cubes $R$ of $Q_n$ in which $S\cap R$ is an exact copy of $H$, and we define the $d$-cube density $λ(H,d)$ of $H$ to be the limit as $n$ goes to infinity of $λ(H,d,n)$. We determine $λ(H,d)$ for several configurations in $Q_3$ and $Q_4$ as well as for an infinite family of configurations. There are strong connections with the inducibility of graphs.
