Waring Decompositions of Monomials
By Weronika Buczy'nska, Jaroslaw Buczy'nski, Zach Teitler. 2012
50 citations recorded by the source corpus.
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.
Subfields: Computational Mathematics, Computational Theory and Mathematics, Signal Processing
View Paper: https://www.semanticscholar.org/paper/9a016659ef2f6720bea3dc45bf36caa28fc06f53
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In Computational Mathematics
In Computational Theory and Mathematics
In Signal Processing
Citations in the corpus
- A comparison of different notions of ranks of symmetric tensors (2012, result): “0 ···x αn n ) = Qn 0(αi +1) mini(αi +1) . This example also shows that the decomposition is not unique, since ǫ is any non-zero constant. For more details on rank of monomials see also [15], [32] and [10]; the example above was also shown with different approach in [10, §2] and in [13, Corollary 3.8]”