Waring decompositions of monomials
  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. 
Weronika Buczy\'nska, Jaros{\l}aw Buczy\'nski, Zach Teitler
math.AG