From symbolic ultrametrics to 3-way maps
Date: 18th Oct. 2017
Speaker: Guillaume Scholz
Institution: School of Computing Sciences, UEA
Organiser: Dr. Michal Mackiewicz
Three-way dissimilarities are a generalization of (two-way) dissimilarities which can be used to indicate the lack of homogeneity or resemblance between any three objects. Here we consider threeway maps which arise from phylogenetic trees whose interior vertices are labelled by an arbitrary set of symbols, which we call tree-maps. Using a parallel between such maps and the notion of a symbolic ultrametrics introduced by Böcker and Dress, we show that, as with two- and three-way tree-metrics and ultrametrics, three-way symbolic tree-maps can be characterized via certain k-point conditions.