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.

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