Geodesic
Axiomatic characterization of transit functions of hierarchies
Ars Mathematica Contemporanea, Tome 14 (2018) no. 1, pp. 117-128.

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Transit functions provide a unifying approach to many results on intervals, convexities, and betweenness. Here we show that hierarchical structures arising in cluster analysis and phylogenetics have a natural characterization in terms of transit functions and that hierarchies are identified by multiple combinations of independent axioms.
DOI : 10.26493/1855-3974.831.e12
Keywords: Transit functions, convexities, hierarchies, rooted trees, axiom systems 
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Manoj Changat; Ferdoos Hossein Nezhad; Peter F. Stadler. Axiomatic characterization of transit functions of hierarchies. Ars Mathematica Contemporanea, Tome 14 (2018) no. 1, pp. 117-128. doi : 10.26493/1855-3974.831.e12. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.831.e12/

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