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    Tree representations of non-symmetric group-valued proximities (1999)

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    Type of Content
    Discussion / Working Papers
    UC Permalink
    http://hdl.handle.net/10092/12576
    
    Publisher
    University of Canterbury
    ISSN
    1172-8531
    Collections
    • Engineering: Reports [732]
    Authors
    Semple, Charles
    Steel, M.
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    Abstract

    Let X be a finite set and let d be a function from X x X into an arbitrary group Q. An example of such a function arises by taking a tree T whose vertices include X, assigning two elements of Q to each edge of T ( one for each orientation of the edge), and setting d(i,j) equal to the product of the elements along the directed path from i to j. We characterize conditions when an arbitrary function d can be represented in this way, and show how such a representation may be explicitly constructed. We also describe the extent to which the underlying tree and the edge weightings are unique in such a representation. These results generalize a recent theorem involving undirected edge assignments by an Abelian group. The non-Abelian bi-directed case is of particular relevance to phylogeny reconstruction in molecular biology.

    ANZSRC Fields of Research
    49 - Mathematical sciences::4901 - Applied mathematics::490102 - Biological mathematics
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    All Rights Reserved
    https://canterbury.libguides.com/rights/theses

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