{"ID":2897270,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.06437","arxiv_id":"2507.06437","title":"Binomiality of colored Gaussian models","abstract":"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.","short_abstract":"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 structu...","url_abs":"https://arxiv.org/abs/2507.06437","url_pdf":"https://arxiv.org/pdf/2507.06437v1","authors":"[\"Benjamin Biaggi\",\"Jan Draisma\",\"Magdaléna Mišinová\"]","published":"2025-07-08T22:39:47Z","proceeding":"math.CO","tasks":"[\"math.CO\",\"math.AG\",\"math.ST\"]","methods":"[]","has_code":false}