An exponential lower bound for the sum of powers of bounded degree polynomials

@article{Kayal2012AnEL,
  title={An exponential lower bound for the sum of powers of bounded degree polynomials},
  author={Neeraj Kayal},
  journal={Electronic Colloquium on Computational Complexity (ECCC)},
  year={2012},
  volume={19},
  pages={81}
}
  • Neeraj Kayal
  • Published 2012 in Electronic Colloquium on Computational Complexity
In this work we consider representations of multivariate polynomials in F[x] of the form f(x) = Q1(x)1 +Q2(x)2 + . . .+Qs(x) , where the ei’s are positive integers and the Qi’s are arbitary multivariate polynomials of degree at most d. We give an explicit n-variate polynomial f of degree n such that any representation of the above form for f requires the number of summands s to be 2Ω( n d ). We also give a asymptotically matching upper bound of 2O( n d ). 
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