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|
|Deposited By:||Prof Alexandre Borovik|
|Deposited On:||10 February 2008|