Waring decompositions of monomials

Journal of Algebra

Volumn 378, Issue , 2013, Pages 45-57

  Buczyńska, Weronika ^a   Buczyński, Jarosław ^a,b   Teitler, Zach ^c  

^a INSTITUTE OF MATHEMATICS   (Poland)

^b INSTITUT FOURIER   (France)

^c BOISE STATE UNIVERSITY   (United States)

Author keywords

Canonical forms; Variety of sums of powers; Waring decomposition; Waring rank

Indexed keywords

EID: 84872345217     PISSN: 00218693     EISSN: 1090266X     Source Type: Journal    
DOI: 10.1016/j.jalgebra.2012.12.011     Document Type: Article

References (15)

1. Carlini Enrico, Catalisano Maria Virginia, Geramita Anthony V. The solution to Waring's problem for monomials. J. Algebra 2012, 370:5-14.
2. Comas Gonzalo, Seiguer Malena On the rank of a binary form. Found. Comput. Math. 2011, 11(1):65-78. MR 2754189.
3. Eisenbud David Commutative Algebra. Grad. Texts in Math. 1995, vol. 150. Springer-Verlag, New York, with a view toward algebraic geometry.
4. Iarrobino Anthony, Kanev Vassil Power Sums, Gorenstein Algebras, and Determinantal Loci. Lecture Notes in Math. 1999, vol. 1721. Springer-Verlag, Berlin, Appendix C by Iarrobino and Steven L. Kleiman, MR 1735271 (2001d:14056).
5. Iliev Atanas, Ranestad Kristian K3 surfaces of genus 8 and varieties of sums of powers of cubic fourfolds. Trans. Amer. Math. Soc. 2001, 353(4):1455-1468. MR 1806733 (2002c:14082).
6. Landsberg J.M. Tensors: Geometry and Applications. Grad. Stud. Math. 2011, vol. 128. Amer. Math. Soc., Providence.
7. Landsberg J.M., Teitler Zach On the ranks and border ranks of symmetric tensors. Found. Comput. Math. 2010, 10(3):339-366.
8. Mella Massimiliano Base loci of linear systems and the Waring problem. Proc. Amer. Math. Soc. 2009, 137(1):91-98. MR 2439429 (2009g:14072).
9. Mukai Shigeru Fano 3-folds. London Math. Soc. Lecture Note Ser. 1992, vol. 179:255-263. Cambridge Univ. Press, Cambridge, MR 1201387 (94a:14042).
10. Oldenburger Rufus Polynomials in several variables. Ann. of Math. (2) 1940, 41:694-710. MR 0001948 (1,324c).
11. Bruce Reznick, On the length of binary forms, in: Quadratic and Higher Degree Forms, in: Dev. Math., Springer, in press.
12. Kristian Ranestad, Symmetric tensor decompositions, Slides from talk at MEGA 2011, May 2011.
13. Ranestad Kristian, Schreyer Frank-Olaf Varieties of sums of powers. J. Reine Angew. Math. 2000, 525:147-181. MR 1780430 (2001m:14009).
14. Ranestad Kristian, Schreyer Frank-Olaf On the rank of a symmetric form. J. Algebra 2011, 346:340-342.
15. J.J. Sylvester, An essay on canonical forms, supplement to a sketch of a memoir on elimination, transformation and canonical forms, Mathematical Papers, 1851, Paper 34 in vol. 1 (publ. 1904), pp. 203-216.