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Date: 9-8-2020
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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 .
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.
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