Gross–Mansour–Tucker conjecture on partial duality polynomials of orientable ribbon graphs

A ribbon graph is orientable if its associated ribbon surface is orientable, and its partial duality polynomial is the generating function that enumerates its partial duals by Euler genus. A polynomial is non-constant with only one non-zero coefficient if exactly one coefficient is non-zero and the polynomial is not constant. Gross–Mansour–Tucker conjecture. There is no orientable ribbon graph having a non-constant partial duality polynomial with only one non-zero coefficient. The conjecture concerns restrictions on the possible partial-duality polynomials of orientable ribbon graphs; it was proposed by Gross, Mansour and Tucker in connection with their introduction of the partial duality polynomial.