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august 2020 Combinatorial properties of ultrametrics and generalized ultrametrics
Oleksiy Dovgoshey
Bull. Belg. Math. Soc. Simon Stevin 27(3): 379-417 (august 2020). DOI: 10.36045/bbms/1599616821

Abstract

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 \emph{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.

Citation

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Oleksiy Dovgoshey. "Combinatorial properties of ultrametrics and generalized ultrametrics." Bull. Belg. Math. Soc. Simon Stevin 27 (3) 379 - 417, august 2020. https://doi.org/10.36045/bbms/1599616821

Information

Published: august 2020
First available in Project Euclid: 9 September 2020

MathSciNet: MR4146738
Digital Object Identifier: 10.36045/bbms/1599616821

Subjects:
Primary: 54E35
Secondary: 06A05, 06A06

Rights: Copyright © 2020 The Belgian Mathematical Society

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Vol.27 • No. 3 • august 2020
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