Logarithmically concave sequence

In mathematics, a sequence a = (a0, a1, ..., an) of nonnegative real numbers is called a logarithmically concave sequence, or a log-concave sequence for short, if ai2 ≥ ai−1ai+1 holds for 0 < i < n .

Remark: some authors (explicitly or not) add two further conditions in the definition of log-concave sequences: These conditions mirror the ones required for log-concave functions.

Refer to chapter 2 of [1] for a discussion on the two notions.

For instance, the sequence (1,1,0,0,1) satisfies the concavity inequalities but not the internal zeros condition.

Examples of log-concave sequences are given by the binomial coefficients along any row of Pascal's triangle and the elementary symmetric means of a finite sequence of real numbers.