论文标题
当所有排列都是组合相似性时
When all Permutations are Combinatorial Similarities
论文作者
论文摘要
令$（x，d）$为半权限的空间。如果存在$ f \ colon d（x^2）\ to d（x^2）$，则$ x $的排列$φ$是$（x，d）$的组合自我相似性，例如$ x $ x $，$ x $，$ x $ y \ y \ y y \ y y \ y y \ y y \ y \ y y \我们描述了任意非空置集合$ y $的所有半学分$ρ$的集合，$ y $的每个排列都是$（y，ρ）$的组合自我相似性。
Let $(X, d)$ be a semimetric space. A permutation $Φ$ of the set $X$ is a combinatorial self similarity of $(X, d)$ if there is a bijective function $f \colon d(X^2) \to d(X^2)$ such that $$ d(x, y) = f(d(Φ(x), Φ(y))) $$ for all $x$, $y \in X$. We describe the set of all semimetrics $ρ$ on an arbitrary nonempty set $Y$ for which every permutation of $Y$ is a combinatorial self similarity of $(Y, ρ)$.
