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2011 Toward a Salmon Conjecture
Daniel J. Bates, Luke Oeding
Experiment. Math. 20(3): 358-370 (2011).

Abstract

Methods from numerical algebraic geometry are applied in combination with techniques from classical representation theory to show that the variety of 3 × 3 × 4 tensors of border rank 4 is cut out by polynomials of degree 6 and 9. Combined with results of Landsberg and Manivel, this furnishes a computational solution of an open problem in algebraic statistics, namely, the set-theoretic version of Allman’s salmon conjecture for 4 × 4 × 4 tensors of border rank 4. A proof without numerical computation was given recently by Friedland and Gross.

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Daniel J. Bates. Luke Oeding. "Toward a Salmon Conjecture." Experiment. Math. 20 (3) 358 - 370, 2011.

Information

Published: 2011
First available in Project Euclid: 6 October 2011

zbMATH: 1262.14056
MathSciNet: MR2836258

Subjects:
Primary: 13A50 , 14L30 , 14M12 , 14Q99 , 15A69 , 15A72 , 20G05 , 65H10 , 68W30

Keywords: Algebraic statistics , Bertini , numerical algebraic geometry , representation theory , Salmon conjecture

Rights: Copyright © 2011 A K Peters, Ltd.

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Vol.20 • No. 3 • 2011
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