Type: Article

On the log-concavity of the degenerate Bernoulli numbers

Florian Luca; Paul Thomas Young;

Abstract:

The degenerate Bernoulli numbers beta(n)(lambda) are polynomials with rational coefficients of degree n in the variable lambda, which arise in several combinatorial settings. An appropriate change of variable transforms beta(n)(lambda) into a polynomial whose coefficients are all positive. Here, we prove that this transformed polynomial is log-concave, and therefore unimodal. As a consequence, we deduce bounds on the absolute values of the roots of beta(n)(lambda).