Grassmann--Plücker functions for orthogonal matroids
Abstract
We present a new cryptomorphic definition of orthogonal matroids with coefficients using Grassmann--Plücker functions. The equivalence is motivated by Cayley's identities expressing principal and almost-principal minors of a skew-symmetric matrix in terms of its Pfaffians. As a corollary of the new cryptomorphism, we deduce that each component of the orthogonal Grassmannian is parameterized by certain part of the Plücker coordinates.
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 27 January 2026
- Document type
- Preprint