Oriented Lagrangian Matroids
Copyright policy )Oriented Lagrangian Matroids
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.
20 pages. To appear in the European Journal of Combinatorics
- University of Florida United States
- University of Salford United Kingdom
- University of Florida United States
- Rutgers, The State University of New Jersey United States
Axiomatic and generalized convexity, Oriented matroids in discrete geometry, delta-matroids, Combinatorial aspects of matroids and geometric lattices, basis polytopes, Lagrangian matroids, symplectic matroids, Coxeter matroids, Theoretical Computer Science, Computational Theory and Mathematics, oriented matroids, FOS: Mathematics, Mathematics - Combinatorics, Geometry and Topology, Combinatorics (math.CO)
Axiomatic and generalized convexity, Oriented matroids in discrete geometry, delta-matroids, Combinatorial aspects of matroids and geometric lattices, basis polytopes, Lagrangian matroids, symplectic matroids, Coxeter matroids, Theoretical Computer Science, Computational Theory and Mathematics, oriented matroids, FOS: Mathematics, Mathematics - Combinatorics, Geometry and Topology, Combinatorics (math.CO)
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