Gross–Mansour–Tucker interpolation conjecture for non-orientable ribbon graphs

Let $G$ be a non-orientable ribbon graph, and define its partial-dual Euler-genus polynomial by

$${}^{\partial}\varepsilon_G(z)=\sum_{A\subseteq E(G)}z^{\varepsilon(G^A)}.$$

A polynomial is interpolating when its non-zero coefficients are all equal to $1$. Gross–Mansour–Tucker interpolation conjecture. The partial-dual Euler-genus polynomial

$${}^{\partial}\varepsilon_G(z)$$

for any non-orientable ribbon graph is interpolating. The paper reports a counterexample and constructs an infinite family of counterexamples, so the conjecture is refuted.