  Let $X$, $Y$ be sets and let $\Phi$, $\Psi$ be mappings with domains $X^{2}$
and $Y^{2}$ respectively. We say that $\Phi$ and $\Psi$ are combinatorially
similar if there are bijections $f \colon \Phi(X^2) \to \Psi(Y^{2})$ and $g
\colon Y \to X$ such that $\Psi(x, y) = f(\Phi(g(x), g(y)))$ 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.
