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arXiv · 2105.00016

Universality of high-strength tensors

Arthur Bik·Alessandro Danelon·Jan Draisma·Rob H. Eggermont
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Abstract

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.

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Arthur Bik, Alessandro Danelon, Jan Draisma, Rob H. Eggermont. 2021-04-30. Universality of high-strength tensors. https://doi.org/10.1007/s10013-021-00522-7

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