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 hypotheses in the definition of log-concave sequences:
These hypotheses mirror the ones required for log-concave functions.
Sequences that fulfill the three conditions are also called Pòlya Frequency sequences of order 2. Refer to chapter 2 of for a discussion on the two notions.
For instance, the sequence checks 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.