On Patchworks and Hierarchies
Andreas Dress, Vincent Moulton, Mike Steel, Taoyang Wu
TL;DR
This paper explores advanced set systems called patchworks and their variants, analyzing their combinatorial properties and introducing a new duality theory for cluster systems based on compatibility, inspired by biological classification.
Contribution
It introduces and studies the properties of various patchwork set systems and proposes a novel duality theory for cluster systems based on compatibility.
Findings
Characterization of different patchwork classes
Development of a duality theory for cluster systems
Insights into combinatorial properties related to biological classification
Abstract
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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Taxonomy
TopicsRough Sets and Fuzzy Logic · semigroups and automata theory · Fractal and DNA sequence analysis