Logarithmically concave sequence

In mathematics, a sequence a₀, a₁, ..., a_n of nonnegative real numbers is called a logarithmically concave sequence, or a log-concave sequence for short, if a_i² > a_i−1a_i+1 holds for 1 < i < n − 1.

Examples of log-concave sequences are given by the binomial coefficients along any row of Pascal's triangle.

References

• Stanley, R. P. (December 1989). "Log-Concave and Unimodal Sequences in Algebra, Combinatorics, and Geometry". Annals of the New York Academy of Sciences 576: 500–535. doi:10.1111/j.1749-6632.1989.tb16434.x. 

See also

• Unimodality
• Logarithmically concave function
• Logarithmically concave measure