Grassmann--Pl\"ucker functions for orthogonal matroids
Combinatorics
2026-02-03 v2
Abstract
We present a new cryptomorphic definition of orthogonal matroids with coefficients using Grassmann--Pl\"ucker 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 Pl\"ucker coordinates.
Keywords
Cite
@article{arxiv.2601.19830,
title = {Grassmann--Pl\"ucker functions for orthogonal matroids},
author = {Changxin Ding and Donggyu Kim},
journal= {arXiv preprint arXiv:2601.19830},
year = {2026}
}