Combinatorial properties of ultrametrics and generalized ultrametrics

O. Dovgoshey

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arXiv · 1908.08349

Combinatorial properties of ultrametrics and generalized ultrametrics

O. Dovgoshey

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Abstract

Let $X$, $Y$ be sets and let $Φ$, $Ψ$ be mappings with domains $X^{2}$ and $Y^{2}$ respectively. We say that $Φ$ and $Ψ$ are combinatorially similar if there are bijections $f \colon Φ(X^2) \to Ψ(Y^{2})$ and $g \colon Y \to X$ such that $Ψ(x, y) = f(Φ(g(x), g(y)))$ for all $x$, $y \in Y$. Conditions under which a given mapping is combinatorially similar to an ultrametric or a pseudoultrametric are found. Combinatorial characterizations are also obtained for poset-valued ultrametric distances recently defined by Priess-Crampe and Ribenboim.

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O. Dovgoshey. 2019-08-22. Combinatorial properties of ultrametrics and generalized ultrametrics. https://arxiv.org/abs/1908.08349

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