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Affine maps that induce polyhedral complex isomorphisms
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
2000 (English)In: Discrete & Computational Geometry, ISSN 0179-5376, E-ISSN 1432-0444, Vol. 24, no 1, 49-60 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we show that an affine bijection f: T-1 --> T-2 between two polyhedral complexes T-1, T-2, both of which consist of a union of faces of two convex polyhedra P-1 and P-2, necessarily respects the cell-complex structure of T-1 and T-2 inherited from P-1 and P-2, respectively, provided f extends to an affine map from P-1 into P-2. In addition, we present an application of this result within the area of T-theory to obtain a far-reaching generalization of previous results regarding the equivalence of two distinct constructions of the phylogenetic tree associated to "perfect" (that is, treelike) distance data.

Place, publisher, year, edition, pages
2000. Vol. 24, no 1, 49-60 p.
Keyword [en]
split decomposition, combinatorial
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-13679ISI: 000087472600003Scopus ID: 2-s2.0-0034375681OAI: oai:DiVA.org:miun-13679DiVA: diva2:412201
Available from: 2011-04-21 Created: 2011-04-21 Last updated: 2016-10-11Bibliographically approved

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