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arXiv · 2601.19830

Grassmann--Plücker functions for orthogonal matroids

Changxin Ding·Donggyu Kim
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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.

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Changxin Ding, Donggyu Kim. 2026-02-01. Grassmann--Plücker functions for orthogonal matroids. https://arxiv.org/abs/2601.19830

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