On subtensors of high partition rank
| Autor: | Draisma, Jan, Karam, Thomas |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | We prove that for every positive integer $d \ge 2$ there exist polynomial functions $F_d, G_d: \mathbb{N} \to \mathbb{N}$ such that for each positive integer $r$, every order-$d$ tensor $T$ over an arbitrary field and with partition rank at least $G_d(r)$ contains a $F_d(r) \times \cdots \times F_d(r)$ subtensor with partition rank at least $r$. We then deduce analogous results on the Schmidt rank of polynomials in zero or high characteristic. Comment: 10 pages |
| Databáze: | arXiv |
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