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arXiv · 2205.06508

When all Permutations are Combinatorial Similarities

Viktoriia Bilet·Oleksiy Dovgoshey
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Abstract

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 $(Y, ρ)$.

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Viktoriia Bilet, Oleksiy Dovgoshey. 2022-05-13. When all Permutations are Combinatorial Similarities. https://arxiv.org/abs/2205.06508

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