Let rmax(n,d) be the maximum Waring rank for the set of *all* homogeneous polynomials of degree d>0 in n indeterminates with coefficients in an algebraically closed field of characteristic zero. To our knowledge, when n,d >= 3, the value of rmax(n,d) is known only for (n,d)=(3,3),(3,4),(3,5),(4,3). We prove that rmax(3,d)=d^2/4+O(d) as a consequence of the upper bound on rmax(3,d) given by the floor of (d^2+6d+1)/4.
The asymptotic leading term for maximum rank of ternary forms of a given degree / DE PARIS, Alessandro. - In: LINEAR ALGEBRA AND ITS APPLICATIONS. - ISSN 0024-3795. - 500:(2016), pp. 15-29. [10.1016/j.laa.2016.03.012]
The asymptotic leading term for maximum rank of ternary forms of a given degree
DE PARIS, ALESSANDRO
2016
Abstract
Let rmax(n,d) be the maximum Waring rank for the set of *all* homogeneous polynomials of degree d>0 in n indeterminates with coefficients in an algebraically closed field of characteristic zero. To our knowledge, when n,d >= 3, the value of rmax(n,d) is known only for (n,d)=(3,3),(3,4),(3,5),(4,3). We prove that rmax(3,d)=d^2/4+O(d) as a consequence of the upper bound on rmax(3,d) given by the floor of (d^2+6d+1)/4.| File | Dimensione | Formato | |
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