Grassmann--Plücker functions for orthogonal matroids
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914297885491200 |
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| author | Ding, Changxin Kim, Donggyu |
| author_facet | Ding, Changxin Kim, Donggyu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19830 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Grassmann--Plücker functions for orthogonal matroids Ding, Changxin Kim, Donggyu Combinatorics 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. |
| title | Grassmann--Plücker functions for orthogonal matroids |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2601.19830 |