Waring decompositions of monomials
Weronika Buczy\'nska, Jaros{\l}aw Buczy\'nski, Zach Teitler
TL;DR
This paper investigates the structure and uniqueness of Waring decompositions of monomials, establishing connections with complete intersection ideals and providing conditions for uniqueness.
Contribution
It characterizes all Waring decompositions of monomials, relates them to complete intersection ideals, and determines when these decompositions are unique.
Findings
Waring decompositions of monomials are derived from complete intersection ideals.
The dimension of the set of Waring decompositions is explicitly determined.
Conditions for the uniqueness of Waring decompositions up to variable scaling are provided.
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.
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