Logarithmically concave sequence
In mathematics, a sequence = of nonnegative real numbers is called a logarithmically concave sequence, or a log-concave sequence for short, if holds for.
Remark: some authors add two further conditions in the definition of log-concave sequences:
These conditions mirror the ones required for log-concave functions.
Sequences that fulfill the three conditions are also called Pólya Frequency sequences of order 2. Refer to chapter 2 of for a discussion on the two notions. For instance, the sequence 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.