Split decomposition over an abelian group, Part 2: Group-valued split systems with weakly compatible support

Authors:
Andreas Dress
Affiliations:
Department for Combinatorics and Geometry, CAS-MPG Partner Institute for Computational Biology, Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences, Shanghai, China and Max Pl ...
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

Split-decomposition theory deals with relations between R-valued split systems and metrics. In a previous publication (the first of a series of papers on split decomposition over an abelian group), a general conceptual framework has been set up to study these relationships from an essentially algebraic point of view, replacing metrics by certain more general, appropriately defined multivariate maps, and considering group-valued split systems that take their values in an arbitrary abelian group. Here, we make use of this set up and establish the principal results of split-decomposition theory regarding split systems with weakly compatible support within this new algebraic framework.