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Split Decomposition over an Abelian Group Part 1: Generalities
Andreas Dress1, 2
1Department for Combinatorics and Geometry, CAS-MPG Partner Institute and Key Lab for Computational Biology, Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences, 320 Yue Yang Road, Shanghai 200031, P.R.China
2Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22 -26, D 04103 Leipzig, Germany
dress@sibs.ac.cn, dress@mis.mpg.de
Annals of Combinatorics 13 (2) pp.199-232 June, 2009
AMS Subject Classification: 05C05, 92D15
Abstract:
Split-decomposition theory deals with relations between $\R$-valued split systems and metrics. Here, we generalize (parts of) this theory, considering group-valued split systems that take their values in an arbitrary abelian group, and replacing metrics by certain, appropriately defined maps (some of which appear to exhibit a decidedly {\em algebraic} flavour). In the second and the third parts of this series of papers, the main results of split-decomposition theory will be established within this conceptual framework.
Keywords: splits, split decomposition, split systems, set systems, group-valued split systems, group-valued set systems, phylogenetic analysis, metrics, bilinear maps, groupoid

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