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2008.13: Metric matroids and metric buildings

2008.13: Alexandre V. Borovik (2008) Metric matroids and metric buildings.

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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 2000 > 05 Combinatorics
MIMS number:2008.13
Deposited By:Prof Alexandre Borovik
Deposited On:10 February 2008

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