On the Waring problem for polynomial rings

@article{Frberg2012OnTW,
  title={On the Waring problem for polynomial rings},
  author={R. Fr{\"o}berg and G. Ottaviani and B. Shapiro},
  journal={Proceedings of the National Academy of Sciences},
  year={2012},
  volume={109},
  pages={5600 - 5602}
}
In this note we discuss an analog of the classical Waring problem for . Namely, we show that a general homogeneous polynomial of degree divisible by k≥2 can be represented as a sum of at most kn k-th powers of homogeneous polynomials in . Noticeably, kn coincides with the number obtained by naive dimension count. 
Monomials as Sums of k th-Powers of Forms
On generic and maximal k-ranks of binary forms
Lower Bounds for Sums of Powers of Low Degree Univariates
On a class of power ideals
Waring rank of binary forms, harmonic cross-ratio and golden ratio
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1
2
3
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References

SHOWING 1-10 OF 24 REFERENCES
The strict Waring problem for polynomial rings
On the Alexander–Hirschowitz theorem
Combinatorics and geometry of power ideals
Varieties of sums of powers
Polynomial interpolation in several variables
Inverse System of a Symbolic Power II. The Waring Problem for Forms
Algebraic boundaries of Hilbert’s SOS cones
Trees, parking functions, syzygies, and deformations of monomial ideals
...
1
2
3
...