Die Erbenhaftung im römischen Recht

系统发育分析越来越多地采用复杂的数学工具，从马尔可夫过程的随机建模，主成分分析，或整数规划到组合学的各个分支，包括极值组合学和多变量关系的组合分析，特别是那些来自（不）相似性数据。这里提出的工作将处理后一个主题，也就是说，它将处理一些基本的组合问题，出现在相当自然的遗传动机的聚类分析。预计解决这些问题将最终导致更好和更快的算法，用于确定推定的分支和阐明虚假的系统发育关系。更具体地说，（1）我们想研究布尼曼复合物的面晶格的各种特定的组合特征，这些特征可以用来模拟例如从网状进化中产生的系统发育网络，（2）我们希望扩展分裂分解技术，以便考虑部分（以及总）分裂，以阐明虚假的系统发育关系和（3）我们坚信，并希望表明，一个k-定义在一个n-集合上的相容和弱相容分裂系统的基数至多为2kn-（2k+1），达到这个基数的分裂系统必然是循环的.

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.