Counter Example to a Strong Matroid Minor Conjecture
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916509280894976 |
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| author | Kumar, Shrawan |
| author_facet | Kumar, Shrawan |
| contents | The main result of this note asserts that a strong form of the Matroid Minor Conjecture due to J. Draisma is not true, i.e., there exist properly ascending chains of $S_\infty$-stable ideals in the affine coordinate ring of the affine infinite Grassmannian, where $S_\infty$ is the infinite symmetric group. In fact, we explicitly construct such an ascending chain. His conjectures on topological noetherian property for the affine infinite Grassmannian remain open though. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_04288 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Counter Example to a Strong Matroid Minor Conjecture Kumar, Shrawan Combinatorics Algebraic Geometry 05B35, 05C25, 05C83, 14N10, 14M15 The main result of this note asserts that a strong form of the Matroid Minor Conjecture due to J. Draisma is not true, i.e., there exist properly ascending chains of $S_\infty$-stable ideals in the affine coordinate ring of the affine infinite Grassmannian, where $S_\infty$ is the infinite symmetric group. In fact, we explicitly construct such an ascending chain. His conjectures on topological noetherian property for the affine infinite Grassmannian remain open though. |
| title | Counter Example to a Strong Matroid Minor Conjecture |
| topic | Combinatorics Algebraic Geometry 05B35, 05C25, 05C83, 14N10, 14M15 |
| url | https://arxiv.org/abs/2412.04288 |