Equations for Lower Bounds on Border Rank

XXX

• Bates , [Bates and Oeding 11] D. and Oeding , L. 2011 . Toward a Salmon Conjecture . Exp. Math. , 20 ( 3 ) : 358 – 370 .
   Web of Science ®Google Scholar
• Bates , [Bates et al. 06] Daniel J. , Hauenstein , Jonathan D. , Sommese , Andrew J. and Wampler , Charles W. 2006 . “ Bertini: Software for Numerical Algebraic Geometry ” .
   Google Scholar
• Blekherman , [Blekherman et al. 12] G. , Hauenstein , J. , Ottem , J. C. , Ranestad , K. and Sturmfels , B. 2012 . Algebraic Boundaries of Hilbert's SOS Cones . Compositio Mathematica , 148 : 1717 – 1735 .
   Web of Science ®Google Scholar
• Bürgisser , [Bürgisser and Ikenmeyer 11] Peter and Ikenmeyer , Christian . Geometric Complexity Theory and Tensor Rank . Proceedings 43rd Annual ACM Symposium on Theory of Computing 2011 , pp. 509 – 518 .
   Google Scholar
• Bürgisser , [Bürgisser et al. 97] Peter , Clausen , Michael and Shokrollahi , M. Amin . 1997 . Algebraic Complexity Theory , Grundlehren der Mathematischen Wissenschaften 315. Springer-Verlag .
   Google Scholar
• Bürgisser , [Bürgisser et al. 13] Peter , Clausen , Michael and Shokrollahi , M. Amin . Explicit Lower Bounds via Geometric Complexity Theory . Proceedings 45th Annual ACM Symposium on Theory of Computing 2013 , pp. 141 – 150 .
   Google Scholar
• Fulton , [Fulton 97] William . 1997 . Young Tableaux , Cambridge University Press . London Mathematical Society Student Texts 35
   Google Scholar
• Fulton , [Fulton and Harris 91] William and Harris , Joe . 1991 . Representation Theory , Springer-Verlag . Graduate Texts in Mathematics 129
   Google Scholar
• Griffin , [Griffin et al. 14] Z. A. , Hauenstein , J. D. , Peterson , C. and Sommese , A. J. “ Numerical Computation of the Hilbert Function of a Zero-Scheme ” . Available online (www.math.ncsu.edu/ ∼jdhauens/preprints). To appear in Springer Proc. Math. Stat., 2014
   Google Scholar
• Hauenstein , [Hauenstein and Sommese 10] J. D. and Sommese , A. J. 2010 . Witness Sets of Projections . Appl. Math. Comput. , 217 : 3349 – 3354 .
   Web of Science ®Google Scholar
• Hauenstein , [Hauenstein and Sommese 13] J. D. and Sommese , A. J. 2013 . Membership Tests for Images of Algebraic Sets by Linear Projections . Appl. Math. Comput. , : 6809 – 6818 .
   Web of Science ®Google Scholar
• Hauenstein , [Hauenstein et al. 12] J. D. , He , Y.-H. and Mehta , D. 2012 . “ Numerical Analyses on Moduli Space of Vacua ” . arXiv:1210.6038
   Google Scholar
• Ikenmeyer , [Ikenmeyer 12] Christian . 2012 . “ Geometric Complexity Theory, Tensor Rank, and Littlewood–Richardson Coefficients ” . PhD thesis, Institute of Mathematics, University of Paderborn .
   Google Scholar
• Landsberg , [Landsberg 04] J. M. 2004 . “ The Border Rank of the Multiplication of 2 × 2 Matrices Is Seven ” . arXiv:math/0407224
   Google Scholar
• Landsberg , [Landsberg 06] J. M. 2006 . The Border Rank of the Multiplication of 2 × 2 Matrices Is Seven . J. Amer. Math. Soc. , 19 : 447 – 459 .
   Web of Science ®Google Scholar
• Landsberg , [Landsberg 12] J. M. 2012 . “ Explicit Tensors of Border Rank at Least 2n –1 ” . arXiv:1209.1664
   Google Scholar
• Landsberg , [Landsberg 12] J. M. 2012 . Tensors: Geometry and Applications , American Mathematical Society . Graduate Studies in Mathematics 128
   Google Scholar
• Landsberg , [Landsberg and Manivel 04] J. M. and Manivel , Laurent . 2004 . On the Ideals of Secant Varieties of Segre Varieties . Found. Comput. Math. , 4 : 397 – 422 .
   Web of Science ®Google Scholar
• Landsberg , [Landsberg and Ottaviani 11] J. M. and Ottaviani , Giorgio . 2011 . New Lower Bounds for the Border Rank of Matrix Multiplication arXiv:1112.6007
   Google Scholar
• Migliore , [Migliore 98] J. C. 1998 . Introduction to Liaison Theory and Deficiency Modules Birkhäuser Progress in Mathematics 165
   Google Scholar
• Schönhage , [Schönhage 81] A. 1981 . Partial and Total Matrix Multiplication . SIAM J. Comput. , 10 : 434 – 455 .
   Web of Science ®Google Scholar
• Sommese , [Sommese and Wampler 05] A. J. and Wampler , C. W. II . 2005 . The Numerical Solution of Systems of Polynomials , World Scientific .
   Google Scholar
• Sommese , [Sommese et al. 01] A. J. , Verschelde , J. and Wampler , C. W. “ Using Monodromy to Decompose Solution Sets of Polynomial Systems into Irreducible Components ” . In Applications of Algebraic Geometry to Coding Theory, Physics and Computation (Eilat, 2001) , 297 – 315 . NATO Sci. Ser. II Math. Phys. Chem. 36 . Kluwer Acad. Publ., 2001
   Google Scholar
• Sommese , [Sommese et al. 02] A. J. , Verschelde , J. and Wampler , C. W. 2002 . Symmetric Functions Applied to Decomposing Solution Sets of Polynomial Systems . SIAM J. Numer. Anal. , 40 : 2026 – 2046 .
   Google Scholar
• Strassen , [Strassen 69] Volker . 1969 . Gaussian Elimination Is Not Optimal. Numer. Math. , 13 : 354 – 356 .
   Web of Science ®Google Scholar