Tree representations of non-symmetric group-valued proximities
| dc.contributor.author | Semple, Charles | |
| dc.contributor.author | Steel, M. | |
| dc.date.accessioned | 2016-08-14T23:10:58Z | |
| dc.date.available | 2016-08-14T23:10:58Z | |
| dc.date.issued | 1999 | en |
| dc.description.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. | en |
| dc.identifier.issn | 1172-8531 | |
| dc.identifier.uri | http://hdl.handle.net/10092/12576 | |
| dc.language.iso | en | |
| dc.publisher | University of Canterbury | en |
| dc.rights | All Rights Reserved | en |
| dc.rights.uri | https://canterbury.libguides.com/rights/theses | |
| dc.subject.anzsrc | Fields of Research::49 - Mathematical sciences::4901 - Applied mathematics::490102 - Biological mathematics | en |
| dc.title | Tree representations of non-symmetric group-valued proximities | en |
| dc.type | Discussion / Working Papers | |
| uc.college | Faculty of Engineering | |
| uc.department | School of Engineering | en |