On Patchworks and Hierarchies

Details On Patchworks and Hierarchies On Patchworks and Hierarchies

2012-02-11

arxiv.org/abs/1202.2460v1

Biology

Quantitative Biology

Populations and Evolution

17 pages, 2 figures

Scientific paper

Motivated by questions in biological classification, we discuss some elementary combinatorial and computational properties of certain set systems that generalize hierarchies, namely, 'patchworks', 'weak patchworks', 'ample patchworks' and 'saturated patchworks' and also outline how these concepts relate to an apparently new 'duality theory' for cluster systems that is based on the fundamental concept of 'compatibility' of clusters.

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