### 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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