On the dimension of the strongly robust complex for configurations in general position
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909826738552832 |
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| author | Kosta, Dimitra Thoma, Apostolos Vladoiu, Marius |
| author_facet | Kosta, Dimitra Thoma, Apostolos Vladoiu, Marius |
| contents | Strongly robust toric ideals are the toric ideals for which the set of indispensable binomials is the Graver basis. The strongly robust simplicial complex $Δ_T$ of a simple toric ideal $I_T$ determines the strongly robust property for all toric ideals that have $I_T$ as their bouquet ideal. We prove that $\text{dim} Δ_T<\text{rank}(T)$ for configurations in general position, partially answering a question posed by Sullivant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04730 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the dimension of the strongly robust complex for configurations in general position Kosta, Dimitra Thoma, Apostolos Vladoiu, Marius Commutative Algebra Algebraic Geometry Combinatorics 05E45, 13F65, 13P10, 14M25 Strongly robust toric ideals are the toric ideals for which the set of indispensable binomials is the Graver basis. The strongly robust simplicial complex $Δ_T$ of a simple toric ideal $I_T$ determines the strongly robust property for all toric ideals that have $I_T$ as their bouquet ideal. We prove that $\text{dim} Δ_T<\text{rank}(T)$ for configurations in general position, partially answering a question posed by Sullivant. |
| title | On the dimension of the strongly robust complex for configurations in general position |
| topic | Commutative Algebra Algebraic Geometry Combinatorics 05E45, 13F65, 13P10, 14M25 |
| url | https://arxiv.org/abs/2510.04730 |