Symmetric sums of squares over k-subset hypercubes

@article{Raymond2018SymmetricSO,
  title={Symmetric sums of squares over k-subset hypercubes},
  author={Annie Raymond and James Saunderson and Mohit Singh and Rekha R. Thomas},
  journal={Mathematical Programming},
  year={2018},
  volume={167},
  pages={315-354}
}
  • Annie Raymond, James Saunderson, +1 author Rekha R. Thomas
  • Published 2018
  • Mathematics, Computer Science
  • Mathematical Programming
  • We consider the problem of finding sum of squares (sos) expressions to establish the non-negativity of a symmetric polynomial over a discrete hypercube whose coordinates are indexed by the k-element subsets of [n]. For simplicity, we focus on the case $$k=2$$k=2, but our results extend naturally to all values of $$k \ge 2$$k≥2. We develop a variant of the Gatermann–Parrilo symmetry-reduction method tailored to our setting that allows for several simplifications and a connection to flag algebras… CONTINUE READING

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