Borovik, Alexandre (2008) Metric matroids and metric buildings. [MIMS Preprint]
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Abstract
These notes represent fragments of an old joint work with I. M. Gelfand; I put in them some material which did not find its way in our book with Neil White "Coxeter Matroids", but, I believe, deserves to be documented. In particular, I use the old term "W-matroid" for what later became a "Coxeter matroid for Coxeter group W". We discuss realizations of W-matroids by retractions of buildings and their convexity properties. We define, in terms of metric properties of retractions, some class of geometric objects which includes,as partial cases, buildings and R-trees. For some of these new geometric structures `abstract' convexity properties of retractions have a natural interpretation in terms of usual Euclidean convexity.
| Item Type: | MIMS Preprint |
|---|---|
| Uncontrolled Keywords: | matroid, building, convexity, R-tree |
| Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 05 Combinatorics |
| Depositing User: | Prof Alexandre Borovik |
| Date Deposited: | 10 Feb 2008 |
| Last Modified: | 05 Jan 2018 19:21 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/1030 |
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