论文标题
弱规范图是边缘传递的
Weakly norming graphs are edge-transitive
论文作者
论文摘要
令$ \ MATHCAL {H} $为$ [0,1]^2 $上的有限可测量对称函数类。对于\ Mathcal {h} $的函数$ h \ and agrage $ g $，带有顶点set $ \ {v_1，\ ldots，v_n \} $和edge set set $ e（g）$，define \ [t_g（h）\; = \; \ int \ cdots \ int \ prod _ {\ {v_i，v_j \} \ in E（g）} h（x_i，x_j） \：dx_1 \ cdots dx_n \：。 \]回答Conlon和Lee提出的一个问题，我们证明，要使$ t_g（| h |）^{1/| e（g）|} $成为$ \ MATHCAL {h} $的态度，图$ G $必须是边缘发射的。
Let $\mathcal{H}$ be the class of bounded measurable symmetric functions on $[0,1]^2$. For a function $h \in \mathcal{H}$ and a graph $G$ with vertex set $\{v_1,\ldots,v_n\}$ and edge set $E(G)$, define \[ t_G(h) \; = \; \int \cdots \int \prod_{\{v_i,v_j\} \in E(G)} h(x_i,x_j) \: dx_1 \cdots dx_n \: . \] Answering a question raised by Conlon and Lee, we prove that in order for $t_G(|h|)^{1/|E(G)|}$ to be a norm on $\mathcal{H}$, the graph $G$ must be edge-transitive.
