The authors disprove the Cuttler-Greene-Skandera conjecture by showing H_44 - H_521 is nonnegative on R^3_{≥0} via an explicit sum of 41 squares, despite 44 and 521 being incomparable in dominance order.
Parrilo, and Rekha R
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An SOS counterexample to an inequality of symmetric functions
The authors disprove the Cuttler-Greene-Skandera conjecture by showing H_44 - H_521 is nonnegative on R^3_{≥0} via an explicit sum of 41 squares, despite 44 and 521 being incomparable in dominance order.