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  • 1
    Electronic Resource
    Electronic Resource
    Affine Maps That Induce Polyhedral Complex Isomorphisms (2000)
    Springer
    Discrete & computational geometry 24 (2000), S. 49-60 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004540010034
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A comparison between two distinct continuous models in projective cluster theory: The median and the tight-span construction (1998)
    Springer
    Annals of combinatorics 2 (1998), S. 299-311 
    Details
    ISSN: 0219-3094
    Keywords: 04A03 ; 04A20 ; 05C99 ; 52B99 ; 92B99 ; Buneman graph ; cluster theory ; split systems ; split decomposition ; T-theory ; T-construction ; pairwise compatibility ; weak compatibility ; median networks ; hypercube ; phylogenetic trees ; phylogenetic networks
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is possible to consider two variants of cluster theory: Inaffine cluster theory, one considers collections ofsubsets of a given setX of objects or states, whereas inprojective cluster theory, one considers collections ofsplits (orbipartitions) of that set. In both contexts, it can be desirable to produce acontinuous model, that is, a spaceT encompassing the given setX which represents in a well-specified and more or less parsimonious way all possibleintermediate objects ortransition states compatible with certain restrictions derived from the given collection of subsets or splits. We investigate an interesting and intriguing relationship between two such constructions that appear in the context of projective cluster theory: TheBuneman construction and thetight-span (or justT)construction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01608527
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    Paper (German National Licenses)
    Fulltext
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