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Article

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

Ballico, E. Set Evincing the Ranks with Respect to an Embedded Variety (Symmetric Tensor Rank and Tensor Rank. Mathematics 2018, 6, 140. https://doi.org/10.3390/math6080140

AMA Style

Ballico E. Set Evincing the Ranks with Respect to an Embedded Variety (Symmetric Tensor Rank and Tensor Rank. Mathematics. 2018; 6(8):140. https://doi.org/10.3390/math6080140

Chicago/Turabian Style

Ballico, Edoardo. 2018. "Set Evincing the Ranks with Respect to an Embedded Variety (Symmetric Tensor Rank and Tensor Rank" Mathematics 6, no. 8: 140. https://doi.org/10.3390/math6080140

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