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Annals of Combinatorics 1 (1997) 183-196
Coordinatizing R-Trees in Terms of Universal c-Trees
Werner F. Terhalle
Research Center for Interdisciplinary Studies on Structure Formation
(FSPM)
Bielefeld University, Postbox 10 01 31, 33501 Bielefeld, Germany
terhalle@mathematik.uni-bielefeld.de
Received February 26, 1997
**AMS Subject Classification**:
05B35, 05C05
**
Abstract.** A complete **R**-tree *T* will be constructed
such that, for every *x* \in *T*,
the cardinality of the set of connected components of T\{x} is the same
and equals a pre-given cardinality *c*; by this construction simultaneously
the valuated matroid of the ends of this **R**-tree is given. In addition,
for any arbitrary **R**-tree, an embedding into such a
“universal *c*-tree”
(for suitable *c*) will be constructed.
**Keywords**:
**R**-trees, valuated matroids
**References**
1.
A.W.M. Dress,
*Trees*, *tight extensions of metric spaces, and the cohomological dimension of
certain groups*: *A note on combinatorial properties of metric spaces*,
Adv. Math. 53 (1984) 321–402.
2. A.W.M. Dress, V.L. Moulton, and W.F. Terhalle,
*T-theory --- an overview*,
Europ. J. Combin. 17 (1996) 161–175.
3. A.W.M. Dress and W.F. Terhalle,
*A combinatorial approach to $\wp$-adic geometry*, Part I:
the process of completion,
Geom. Dedicata 46 (1993) 127–148.
4. A.W.M. Dress and W.F. Terhalle,
*The real tree*,
Adv. Math. 120 (1996) 283–301.
5. A.W.M. Dress and W. Wenzel,
*Valuated matroids*,
Adv. Math. 93 (1992) 214–250.
6. W.F. Terhalle,
*Ein kombinatorischer Zugang zu $\wp$-adischer geometrie: bewertete
matroide*, Bäume und Gebäude,
Diss., University Bielefeld, 1992.
7. W.F. Terhalle,
*R-Trees and symmetric differences of sets*,
Europ. J. Combin., to appear.
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