Refined ratio monotonicity of the coordinator polynomials of the root lattice of type Bn

Abstract

Ratio monotonicity, a property stronger than both log-concavity and the spiral property, describes the behavior of the coefficients of many classical polynomials. It is known that the coordinator polynomials of the root lattice of type Bn{B}_{n} possess log-concavity. In this paper, we show that the coordinator polynomials of type Bn{B}_{n} have a refined version of ratio monotonicity except for the first and the last terms. To our knowledge, this refined version is novel.

Keywords

• ratio monotonicity
• coordinator polynomials
• log-concavity
• spiral property
• 05a15
• 05a20
• 11h06