The Ratio Monotonicity of the q-Derangement Numbers
William Y.C. Chen and Ernest X. W. Xia
Abstract: We introduce the notion of ratio monotonicity for polynomials with nonnegative coefficients, and we show that for n ≥ 6, the q-derangement numbers Dn(q) are strictly ratio monotone, except for the last term when n is even. This property implies the spiral property and log-concavity.
AMS Classification: 05A30, 05A15.
Keywords: q-derangement number, spiral property, log-concavity, ratio monotone property.