Die Erbenhaftung im römischen Recht

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Phylogenetic analysis increasingly employs sophisticated mathematical tools ranging from stochastic modelling of Markov processes, principal component analysis, or integer programming to various branches of combinatorics, including extremal combinatorics and combinatorial analysis of multivariate relationships, in particular those derived from (dis)similarity data. The work proposed here will deal with the latter topics, that is, it will deal with some basic combinatorial problems that turn up quite naturally within phylogenetically motivated cluster analysis. It is expected that solving these problems will eventually lead to better and faster algorithms for identifying putative clades and for elucidating spurious phylogenetic relationships. More specifically, (1) we want to study various particular combinatorial features of the face lattice of Buneman complexes that can be used to model phylogenetic nets arising for instance from reticulated evolution, (2) we want to extend split decomposition techniques so as to take into account partial (as well as total) splits to elucidate spurious phylogenetic relationships and (3) we strongly believe and would like to show that a k-compatible and weakly compatible split system defined on an n-set has cardinality at most 2kn-(2k+1) and that those that attain this cardinality are necessarily cyclic.