Gross–Mansour–Tucker conjecture on orientable ribbon graph partial-dual genus polynomials

A ribbon graph is orientable if its underlying surface is orientable, and its partial-dual genus polynomial records the genera of all partial duals. A polynomial is non-constant if it has at least one term of positive degree, and it has only one non-zero coefficient if exactly one coefficient in the polynomial is non-zero. Gross–Mansour–Tucker conjecture. There is no orientable ribbon graph having a non-constant partial-dual genus polynomial with only one non-zero coefficient. This conjecture concerns the possible shapes of partial-dual genus polynomials of orientable ribbon graphs; the source presents it as an open conjecture following known examples for non-orientable ribbon graphs.