Strength and partition rank under limits and field extensions
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866929715406700544 |
|---|---|
| author | Bik, Arthur Draisma, Jan Lampert, Amichai Ziegler, Tamar |
| author_facet | Bik, Arthur Draisma, Jan Lampert, Amichai Ziegler, Tamar |
| contents | The strength of a multivariate homogeneous polynomial is the minimal number of terms in an expression as a sum of products of lower-degree homogeneous polynomials. Partition rank is the analogue for multilinear forms. Both ranks can drop under field extensions, and both can jump in a limit. We show that, for fixed degree and under mild conditions on the characteristic of the ground field, the strength is at most a polynomial in the border strength. We also establish an analogous result for partition rank. Our results control both the jump under limits and the drop under field extensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10007 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strength and partition rank under limits and field extensions Bik, Arthur Draisma, Jan Lampert, Amichai Ziegler, Tamar Algebraic Geometry Computational Complexity Representation Theory The strength of a multivariate homogeneous polynomial is the minimal number of terms in an expression as a sum of products of lower-degree homogeneous polynomials. Partition rank is the analogue for multilinear forms. Both ranks can drop under field extensions, and both can jump in a limit. We show that, for fixed degree and under mild conditions on the characteristic of the ground field, the strength is at most a polynomial in the border strength. We also establish an analogous result for partition rank. Our results control both the jump under limits and the drop under field extensions. |
| title | Strength and partition rank under limits and field extensions |
| topic | Algebraic Geometry Computational Complexity Representation Theory |
| url | https://arxiv.org/abs/2502.10007 |