Metric matroids and metric buildings

Borovik, Alexandre (2008) Metric matroids and metric buildings. [MIMS Preprint]

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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

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