Binomiality of colored Gaussian models
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909681112317952 |
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| author | Biaggi, Benjamin Draisma, Jan Mišinová, Magdaléna |
| author_facet | Biaggi, Benjamin Draisma, Jan Mišinová, Magdaléna |
| contents | Following earlier work by Coons-Maraj-Misra-Sorea and Misra-Sullivant, we study colored, undirected Gaussian graphical models, and present a necessary and sufficient condition for such a model to have binomial vanishing ideal. These conditions involve Jordan schemes, a variant of association schemes, well-known structures in algebraic combinatorics. Using association schemes without transitive group action, we refute the conjecture by Coons-Maraj-Misra-Sorea that binomiality implies that the color classes must be orbits under the automorphism group of the colored graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06437 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Binomiality of colored Gaussian models Biaggi, Benjamin Draisma, Jan Mišinová, Magdaléna Combinatorics Algebraic Geometry Statistics Theory 62R01 Following earlier work by Coons-Maraj-Misra-Sorea and Misra-Sullivant, we study colored, undirected Gaussian graphical models, and present a necessary and sufficient condition for such a model to have binomial vanishing ideal. These conditions involve Jordan schemes, a variant of association schemes, well-known structures in algebraic combinatorics. Using association schemes without transitive group action, we refute the conjecture by Coons-Maraj-Misra-Sorea that binomiality implies that the color classes must be orbits under the automorphism group of the colored graph. |
| title | Binomiality of colored Gaussian models |
| topic | Combinatorics Algebraic Geometry Statistics Theory 62R01 |
| url | https://arxiv.org/abs/2507.06437 |