TY - JOUR
T1 - On generic and maximal k-ranks of binary forms
AU - Lundqvist, Samuel
AU - Oneto, Alessandro
AU - Reznick, Bruce
AU - Shapiro, Boris
N1 - Publisher Copyright:
© 2018 Elsevier B.V.
PY - 2019/5
Y1 - 2019/5
N2 - In what follows, we pose two general conjectures about decompositions of homogeneous polynomials as sums of powers. The first one (suggested by G. Ottaviani) deals with the generic k-rank of complex-valued forms of any degree divisible by k in any number of variables. The second one (by the fourth author) deals with the maximal k-rank of binary forms. We settle the first conjecture in the cases of two variables and the second in the first non-trivial case of the 3-rd powers of quadratic binary forms.
AB - In what follows, we pose two general conjectures about decompositions of homogeneous polynomials as sums of powers. The first one (suggested by G. Ottaviani) deals with the generic k-rank of complex-valued forms of any degree divisible by k in any number of variables. The second one (by the fourth author) deals with the maximal k-rank of binary forms. We settle the first conjecture in the cases of two variables and the second in the first non-trivial case of the 3-rd powers of quadratic binary forms.
UR - http://www.scopus.com/inward/record.url?scp=85052157255&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85052157255&partnerID=8YFLogxK
U2 - 10.1016/j.jpaa.2018.08.015
DO - 10.1016/j.jpaa.2018.08.015
M3 - Article
AN - SCOPUS:85052157255
SN - 0022-4049
VL - 223
SP - 2062
EP - 2079
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
IS - 5
ER -