Group for Research in Decision Analysis

Symmetric sums of squares

Annie Raymond University of Washington, United States

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 /(k/)-element subsets of /([n]/). We develop a variant of the Gatermann-Parrilo symmetry-reduction method tailored to our setting that allows for several simplifications and a connection to Razborov's flag algebras. We show that every symmetric polynomial that has a sos expression of a fixed degree also has a succinct sos expression whose size depends only on the degree and not on the number of variables. This is joint work with James Saunderson, Mohit Singh and Rekha Thomas.

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