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Mathematics 2018, 6(8), 140; https://doi.org/10.3390/math6080140

Set Evincing the Ranks with Respect to an Embedded Variety (Symmetric Tensor Rank and Tensor Rank

Department of Mathematics, University of Trento, 38123 Povo, Italy
Received: 11 July 2018 / Revised: 7 August 2018 / Accepted: 8 August 2018 / Published: 14 August 2018
(This article belongs to the Special Issue Decomposability of Tensors)
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Abstract

Let X P r be an integral and non-degenerate variety. We study when a finite set S X evinces the X-rank of the general point of the linear span of S. We give a criterion when X is the order d Veronese embedding X n , d of P n and | S | ( n + d / 2 n ) . For the tensor rank, we describe the cases with | S | 3 . For X n , d , we raise some questions of the maximum rank for d 0 (for a fixed n) and for n 0 (for a fixed d). View Full-Text
Keywords: X-rank; symmetric tensor rank; tensor rank; veronese variety; segre variety X-rank; symmetric tensor rank; tensor rank; veronese variety; segre variety
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Ballico, E. Set Evincing the Ranks with Respect to an Embedded Variety (Symmetric Tensor Rank and Tensor Rank. Mathematics 2018, 6, 140.

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