Abstract:
We describe in the space of binary forms of degree d the strata of forms having a given rank. We also give a simple algorithm for determining the rank of a given form. © 2010 SFoCM.
Referencias:
- Alexander, J., Hirschowitz, A., Polynomial interpolation in several variables (1995) J. Algebr. Geom., 4 (2), pp. 201-222
- Boij, M., Carlini, E., Geramita, A.V., (2010) Monomials as sums of powers: the real binary case, , arXiv: 1005. 3050v1
- Buczynski, J., Ginesky, A., Landsberg, J.M., (2010) Determinantal equations for secant varieties and the Eisenbud-Koh-Stillman conjecture, , arXiv: 0909. 4865
- Catalisano, M.V., Geramita, A.V., Gimigliano, A., Ranks of tensors, secant varieties of Segre varieties and fat points (2002) Linear Algebra Appl., 355, pp. 263-285
- Causa, A., Re, R., (2010) On the maximum rank of a real binary form, , arXiv: 1006. 5127
- (2002) Mathematics of Quantum Computation. Computational Mathematics Series, , G. Chen and R. K. Brylinski (Eds.), Boca Raton: Chapman & Hall/CRC
- Ciliberto, C., Geometric aspects of polynomial interpolation in more variables and of Waring's problem (2001) European Congress of Mathematics, 201 I, pp. 289-316. , Barcelona2000Progr. Math, Basel: Birkhäuser
- Common, P., Ottaviani, G., (2009) On the typical rank of real binary forms, , arXiv: 0909. 4865
- Elliott, E.B., (1895) An Introduction to the Algebra of Quantics, , Oxford: Clarendon Press
- Grace, J.H., Young, A., (1903) The Algebra of Invariants, , Cambridge: Univ. Press
- Gundelfinger, S., Zur théorie der binaren formen (1886) J. Reine Angew. Math., 100, pp. 413-424
- Harris, J., (1992) Algebraic Geometry, A First Course, , Graduate Texts in Mathematics, Berlin: Springer
- Iarrobino, A., Kanev, V., (1999) Power Sums, Gorenstein Algebras, and Determinantal Loci, 1721. , Lecture Notes in MathematicsAppendix C by Iarrobino and Steven L. Kleiman, Berlin: Springer
- Kung, J.P.S., Canonical forms for binary forms of even degree (1987) Invariant Theory, 1278, pp. 52-61. , Lecture Notes in Math, Berlin: Springer
- Kung, J.P.S., Rota, G.-C., The invariant theory of binary forms (1984) Bull. Am. Math. Soc. (N.S.), 10 (1), pp. 27-85
- Landsberg, J.M., Geometry and the complexity of matrix multiplication (2008) Bull. Am. Math. Soc. (N.S.), 45 (2), pp. 247-284
- Landsberg, J.M., Teitler, Z., On the ranks of tensors and symmetric tensors (2010) Found. Comput. Math., 10 (3), pp. 339-366
- Reznick, B., Homogeneous polynomial solutions to constant coefficient PDE's (1996) Adv. Math., 117 (2), pp. 179-192
- Sylvester, J.J., An essay on canonical forms, supplement to a sketch of a memoir on elimination, transformation and canonical forms (1904) Collected Works, I, pp. 203-216. , Cambridge: Cambridge University Press
- Sylvester, J.J., Sketch of a memoir on elimination, transformation and canonical forms (1904) Collected Works, I, pp. 184-197. , Cambridge: Cambridge University Press
Citas:
---------- APA ----------
Comas, G. & Seiguer, M.
(2011)
. On the Rank of a Binary Form. Foundations of Computational Mathematics, 11(1), 65-78.
http://dx.doi.org/10.1007/s10208-010-9077-x---------- CHICAGO ----------
Comas, G., Seiguer, M.
"On the Rank of a Binary Form"
. Foundations of Computational Mathematics 11, no. 1
(2011) : 65-78.
http://dx.doi.org/10.1007/s10208-010-9077-x---------- MLA ----------
Comas, G., Seiguer, M.
"On the Rank of a Binary Form"
. Foundations of Computational Mathematics, vol. 11, no. 1, 2011, pp. 65-78.
http://dx.doi.org/10.1007/s10208-010-9077-x---------- VANCOUVER ----------
Comas, G., Seiguer, M. On the Rank of a Binary Form. Found. Comput. Math. 2011;11(1):65-78.
http://dx.doi.org/10.1007/s10208-010-9077-x