Oriented Lagrangian Matroids
Combinatorics
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0010237,
title = {Oriented Lagrangian Matroids},
author = {Richard F. Booth and Alexandre V. Borovik and Israel M. Gelfand and Neil White},
journal= {arXiv preprint arXiv:math/0010237},
year = {2007}
}
Comments
20 pages. To appear in the European Journal of Combinatorics