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Les isomorphismes HTS et HTE. (The HTS and HTE isomorphisms). (French) Zbl 0724.05055

Summary: What is called the Benzécri/Johnson bijection links the ultra dissimilarities (ultrametrics) to the strictly indexed hierarchies. In 1984, Diday introduced the pyramids (natural extension of hierarchies for plane visualisation) and he accompanied them with an extension of the Benzécri/Johnson bijection: the associated dissimilarities are the pyras. The same year, Fichet proposed a different extension dealing with all pyramids with a strict subclass of pyras. In 1985, we introduced a bijection between all pyras and strictly indexed prepyramids (not taking the intersection into account).
We present here HTS and HTE ordered set isomorphisms which include the former bijections and can be applied to all dissimilarities. An a priori difficulty was to find a suitable characterization for such image... However, it so happens that when we restrict our theory to symmetrical graphs (dissimilarities of one or two values) we obtain the Gilmore characterization (1960).
In the second article, some interesting subclasses associated by our isomorphisms will be highlighted. (See the following review.)

MSC:

05C65 Hypergraphs
62-07 Data analysis (statistics) (MSC2010)

Citations:

Zbl 0724.05056
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