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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.17826 |
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| _version_ | 1866915128716296192 |
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| author | Boege, Tobias Selover, Jesse Zubkov, Maksym |
| author_facet | Boege, Tobias Selover, Jesse Zubkov, Maksym |
| contents | We analyze a combinatorial rule satisfied by the signs of principal minors of a real symmetric matrix. The sign patterns satisfying this rule are equivalent to uniform oriented Lagrangian matroids. We first discuss their structure and symmetries and then study their asymptotics, proving that almost all of them are not representable by real symmetric matrices. We offer several conjectures and experimental results concerning representable sign patterns and the topology of their representation spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_17826 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sign patterns of principal minors of real symmetric matrices Boege, Tobias Selover, Jesse Zubkov, Maksym Combinatorics Algebraic Geometry 05B20 (primary) 14P10, 14P25, 15A15 (seconary) We analyze a combinatorial rule satisfied by the signs of principal minors of a real symmetric matrix. The sign patterns satisfying this rule are equivalent to uniform oriented Lagrangian matroids. We first discuss their structure and symmetries and then study their asymptotics, proving that almost all of them are not representable by real symmetric matrices. We offer several conjectures and experimental results concerning representable sign patterns and the topology of their representation spaces. |
| title | Sign patterns of principal minors of real symmetric matrices |
| topic | Combinatorics Algebraic Geometry 05B20 (primary) 14P10, 14P25, 15A15 (seconary) |
| url | https://arxiv.org/abs/2407.17826 |