Universality of High-Strength Tensors
| Autor: | Arthur Bik, Rob H. Eggermont, Alessandro Danelon, Jan Draisma |
|---|---|
| Přispěvatelé: | Discrete Algebra and Geometry, Coding Theory and Cryptology |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
Pure mathematics
Polynomial Functor Degree (graph theory) General Mathematics Infinite tensors Universality (philosophy) 510 Mathematik Mathematics - Commutative Algebra Commutative Algebra (math.AC) Polynomial functor Mathematics - Algebraic Geometry 510 Mathematics Corollary Homogeneous polynomial Bounded function FOS: Mathematics Strength Orbit (control theory) GL-varieties Algebraic Geometry (math.AG) Mathematics 14R20 15A21 15A69 |
| Zdroj: | Vietnam Journal of Mathematics, 50(2), 557-580. Springer Bik, Arthur; Danelon, Alessandro; Draisma, Jan; Eggermont, Rob H (2022). Universality of High-Strength Tensors. Vietnam journal of mathematics, 50(2), pp. 557-580. Springer 10.1007/s10013-021-00522-7 |
| ISSN: | 2305-2228 2305-221X |
| Popis: | A theorem due to Kazhdan and Ziegler implies that, by substituting linear forms for its variables, a homogeneous polynomial of sufficiently high strength specialises to any given polynomial of the same degree in a bounded number of variables. Using entirely different techniques, we extend this theorem to arbitrary polynomial functors. As a corollary of our work, we show that specialisation induces a quasi-order on elements in polynomial functors, and that among the elements with a dense orbit there are unique smallest and largest equivalence classes in this quasi-order. Comment: 19 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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