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Linear and Multilinear Algebra Volume 60, 2012 - Issue 6
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Original Articles

On the typical rank of real binary forms

Pierre Comon Lab. I3S, CNRS, University of Nice, BP.121, 2000 route des Lucioles, 06903 Sophia-Antipolis cedex, FranceCorrespondence[email protected]
&
Giorgio Ottaviani Dipartimento di Matematica ‘U. Dini’, Università di Firenze, viale Morgagni 67/A, 50134 Firenze, Italy
Pages 657-667 | Received 15 Oct 2009, Accepted 13 Sep 2011, Published online: 25 Nov 2011

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Alejandro González Nevado & Ettore Teixeira Turatti. (2023) Binary forms of suprageneric rank and the multiple root loci. Communications in Algebra 0:0, pages 1-9.
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E. Ballico. (2014) An upper bound for the real tensor rank and the real symmetric tensor rank in terms of the complex ranks. Linear and Multilinear Algebra 62:11, pages 1546-1552.
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M. Ansola, A. Díaz-Cano & M.A. Zurro. (2021) Semialgebraic sets and real binary forms decompositions. Journal of Symbolic Computation 107, pages 209-220.
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Maria Chiara Brambilla & Giovanni Staglianò. (2020) Algebraic Boundaries Among Typical Ranks for Real Binary Forms of Arbitrary Degree. Foundations of Computational Mathematics 21:4, pages 1003-1022.
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Edoardo Ballico & Emanuele Ventura. (2020) Labels of real projective varieties. Bollettino dell'Unione Matematica Italiana 13:2, pages 257-273.
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Enrico Carlini, Huy Tài Hà, Brian Harbourne & Adam Van TuylEnrico Carlini, Huy Tài Hà, Brian Harbourne & Adam Van Tuyl. 2020. Ideals of Powers and Powers of Ideals. Ideals of Powers and Powers of Ideals 133 133 .
E. Ballico. (2019) Reconstruction of a homogeneous polynomial from its additive decompositions when identifiability fails. Arab Journal of Mathematical Sciences.
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Jinyan FanJiawang Nie & Anwa Zhou. (2019) Completely Positive Binary Tensors. Mathematics of Operations Research 44:3, pages 1087-1100.
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Maria Chiara Brambilla & Giovanni Staglianò. (2018) On the algebraic boundaries among typical ranks for real binary forms. Linear Algebra and its Applications 557, pages 403-418.
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Ralf Fröberg, Samuel Lundqvist, Alessandro Oneto & Boris Shapiro. (2018) Algebraic Stories from One and from the Other Pockets. Arnold Mathematical Journal 4:2, pages 137-160.
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Alessandra Bernardi, Grigoriy Blekherman & Giorgio Ottaviani. (2017) On real typical ranks. Bollettino dell'Unione Matematica Italiana 11:3, pages 293-307.
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Edoardo Ballico & Alessandra Bernardi. (2017) Typical and admissible ranks over fields. Rendiconti del Circolo Matematico di Palermo Series 2 67:1, pages 115-128.
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Jianxin Chen, Andrew M. Childs & Shih-Han Hung. (2018) Quantum algorithm for multivariate polynomial interpolation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474:2209, pages 20170480.
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Alessandra Bernardi, Noah S. Daleo, Jonathan D. Hauenstein & Bernard Mourrain. (2017) Tensor decomposition and homotopy continuation. Differential Geometry and its Applications 55, pages 78-105.
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Neriman Tokcan. (2017) On the waring rank of binary forms. Linear Algebra and its Applications 524, pages 250-262.
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Mateusz Michałek, Hyunsuk Moon, Bernd Sturmfels & Emanuele Ventura. (2016) Real rank geometry of ternary forms. Annali di Matematica Pura ed Applicata (1923 -) 196:3, pages 1025-1054.
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Grigoriy Blekherman & Rainer Sinn. (2016) Real rank with respect to varieties. Linear Algebra and its Applications 505, pages 344-360.
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Yang Qi, Pierre Comon & Lek-Heng Lim. (2016) Semialgebraic Geometry of Nonnegative Tensor Rank. SIAM Journal on Matrix Analysis and Applications 37:4, pages 1556-1580.
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Xinzhen Zhang, Zheng-Hai Huang & Liqun Qi. (2016) Comon's Conjecture, Rank Decomposition, and Symmetric Rank Decomposition of Symmetric Tensors. SIAM Journal on Matrix Analysis and Applications 37:4, pages 1719-1728.
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Hwangrae Lee & Bernd Sturmfels. (2016) Duality of multiple root loci. Journal of Algebra 446, pages 499-526.
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Maurizio Banchi. (2015) Rank and border rank of real ternary cubics. Bollettino dell'Unione Matematica Italiana 8:1, pages 65-80.
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Grigoriy Blekherman. (2013) Typical Real Ranks of Binary Forms. Foundations of Computational Mathematics 15:3, pages 793-798.
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Edoardo Ballico. (2014) ON THE TYPICAL RANK OF REAL POLYNOMIALS (OR SYMMETRIC TENSORS) WITH A FIXED BORDER RANK. Acta Mathematica Vietnamica 39:3, pages 367-378.
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Edoardo Ballico. (2014) On the typical rank of real bivariate polynomials. Linear Algebra and its Applications 452, pages 263-269.
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Pierre Comon. (2014) Tensors : A brief introduction. IEEE Signal Processing Magazine 31:3, pages 44-53.
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Enrico Carlini, Nathan Grieve & Luke Oeding. 2014. Connections Between Algebra, Combinatorics, and Geometry. Connections Between Algebra, Combinatorics, and Geometry 101 146 .
E. Ballico. (2013) Symmetric tensor rank over an infinite field. Arabian Journal of Mathematics 2:4, pages 345-348.
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E. Ballico. (2013) Symmetric Tensor Rank and Scheme Rank: An Upper Bound in terms of Secant Varieties. Geometry 2013, pages 1-3.
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Edoardo Ballico & Alessandra Bernardi. (2013) Real and Complex Rank for Real Symmetric Tensors with Low Ranks. Algebra 2013, pages 1-5.
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Bruce Reznick. 2013. Quadratic and Higher Degree Forms. Quadratic and Higher Degree Forms 207 232 .

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