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# Logarithmically Concave Sequence

A finite sequence of real numbers is said to be logarithmically concave (or log-concave) if

holds for every with .

A logarithmically concave sequence of positive numbers is also unimodal.

If and are two positive log-concave sequences of the same length, then is also log-concave. In addition, if the polynomial has all its zeros real, then the sequence is log-concave (Levit and Mandrescu 2005).

An example of a logarithmically concave sequence is the sequence of binomial coefficients for fixed and .

Logarithmically Concave Function, Logarithmically Concave Polynomial, Unimodal Sequence

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## References

Levit, V. E. and Mandrescu, E. "The Independence Polynomial of a Graph--A Survey." In Proceedings of the 1st International Conference on Algebraic Informatics. Held in Thessaloniki, October 20-23, 2005 (Ed. S. Bozapalidis, A. Kalampakas, and G. Rahonis). Thessaloniki, Greece: Aristotle Univ., pp. 233-254, 2005.

## Referenced on Wolfram|Alpha

Logarithmically Concave Sequence

## Cite this as:

Weisstein, Eric W. "Logarithmically Concave Sequence." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LogarithmicallyConcaveSequence.html