Peeling phylogenetic ‘oranges’ |
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Authors: | Vincent Moulton Mike Steel |
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Institution: | a The Linnaeus Centre for Bioinformatics, Uppsala University, Box 598, 751 24, Uppsala, Sweden;b Biomathematics Research Centre, Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand |
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Abstract: | We investigate the combinatorics of a topological space that is generated by the set of edge-weighted finite trees. This space arises by multiplying the weights of edges on paths in trees and is closely connected to tree reconstruction problems involving finite state Markov processes. We show that this space is a contractible finite CW-complex whose face poset can be described via a partial order on semilabelled forests. We then describe some combinatorial properties of this poset, showing that, for example, it is pure, thin and contractible. |
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Keywords: | Trees Forests Partitions Poset Contractibility |
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