In this paper, we prove the \(q\)-log-convexity of Domb’s polynomials, which was conjectured by Sun in the study of series for powers of \(\pi\). As a result, we obtain the log-convexity of Domb’s numbers. Our proof is based on the \(q\)-log-convexity of Narayana polynomials of type \(B\) and a criterion for determining \(q\)-log-convexity of self-reciprocal polynomials.
Citation
Donna Q.J.Dou, Anne X.Y.Ren. The \(q\)-log-convexity of Domb’s Polynomials[J], Ars Combinatoria, Volume 123. 351-370. .