Carnevale–Voll polynomial nonvanishing conjecture

For positive integers $\lambda_1>\lambda_2$, define

$$C_{\lambda_1,\lambda_2}(x,1)=\sum_{j=0}^{\lambda_2}{\lambda_1\choose j}{\lambda_2\choose j}x^j.$$

Carnevale–Voll conjecture.

$$C_{\lambda_1,\lambda_2}(-1,1)\neq0.$$

This is the formulation of Carnevale and Voll's Conjecture A relevant to the absence of unitary factors in their polynomial. The paper proves the assertion in several parameter ranges and studies its asymptotic validity, while the full conjecture remains open.