Logarithmically concave sequence

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In mathematics, a sequence $a 0, a 1, ..., a n$ of nonnegative real numbers is called a logarithmically concave sequence, or a log-concave sequence for short, if $a i 2 > a i -1 a i +1$ 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

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