5 papers
Lagrangian Matroids: Representations of Type
Richard F. Booth, Alexandre V. Borovik, Neil White
We introduce the concept of orientation for Lagrangian matroids represented in the flag variety of maximal isotropic subspaces of dimension N in the real vector space of dimension…
Lagrangian Pairs and Lagrangian Orthogonal Matroids
Richard F. Booth, Alexandre V. Borovik, Neil White
Represented Coxeter matroids of types and , that is, symplectic and orthogonal matroids arising from totally isotropic subspaces of symplectic or (even-dimensional) orth…
Oriented Lagrangian Orthogonal Matroid Representations
Richard F. Booth
In this paper we extend the theory of oriented matroids to Lagrangian orthogonal matroids and their representations, and give a completely natural transformation from a representat…
Oriented Lagrangian Matroids
Richard F. Booth, Alexandre V. Borovik, Israel M. Gelfand +1
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…
Lagrangian Matroids associated with Maps on Orientable Surfaces
Richard F. Booth, Alexandre V. Borovik, Israel Gelfand
The aim of the paper is to clarify the nature of combinatorial structures associated with maps on closed compact surfaces. We prove that maps give rise to Lagrangian matroids repre…