Existence of a second symmetric power for the Vámos matroid

The question asks whether the Vámos matroid has a second symmetric power. Earlier literature treated the answer as unknown and conjectured that it does not.

Known results

• March 2019: a tropical-ideal obstruction for $U_{2,3}\oplus V_8$ used nonexistence of a suitable quasi-product, but explicitly did not settle $V_8$ itself.
• January 2024: Matroid Products in Tropical Geometry still posed the existence of a second symmetric power for $V_8$ as open, while conjecturing nonexistence.

September 2026 claimed resolution

A preprint listed on September 8, 2026, titled The Vámos Matroid Has No Second Symmetric Power, claims to prove nonexistence and thereby rules out the corresponding tropical-ideal realization. The claim is unrefereed and has not been independently verified in the retrieved material.

Current status (as of September 2026): The question was open through January 2024, while a September 2026 unrefereed preprint now claims a negative answer; verification remains outstanding.