Waring decompositions of monomials
arXiv:1201.2922 · doi:10.1016/j.jalgebra.2012.12.011
Abstract
A Waring decomposition of a polynomial is an expression of the polynomial as a sum of powers of linear forms, where the number of summands is minimal possible. We prove that any Waring decomposition of a monomial is obtained from a complete intersection ideal, determine the dimension of the set of Waring decompositions, and give the conditions under which the Waring decomposition is unique up to scaling the variables.
v2: Improved exposition. v3: Final version; minor changes only. 13 pages