Oriented Lagrangian Matroids

Details Oriented Lagrangian Matroids Oriented Lagrangian Matroids

2000-10-25

arxiv.org/abs/math/0010237v1

Mathematics

Combinatorics

20 pages. To appear in the European Journal of Combinatorics

Scientific paper

In this paper we present a definition of oriented Lagrangian symplectic matroids and their representations. Classical concepts of orientation and this extension may both be thought of as stratifications of thin Schubert cells into unions of connected components. The definitions are made first in terms of a combinatorial axiomatisation, and then again in terms of elementary geometric properties of the Coxeter matroid polytope. We also generalise the concept of rank and signature of a quadratic form to symplectic Lagrangian matroids in a surprisingly natural way.

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