Logarithmically Concave Polynomial

A polynomial is called logarithmically concave (or log-concave) if the sequence of its coefficients is logarithmically concave.

If P(x) is log-convex and Q(x) is unimodal, then P(x)Q(x) is unimodal. However, the product of two log-convex polynomials is itself log-convex (Levit and Mandrescu 2005).

See also

Logarithmically Concave Sequence

Explore with Wolfram|Alpha


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 Polynomial

Cite this as:

Weisstein, Eric W. "Logarithmically Concave Polynomial." From MathWorld--A Wolfram Web Resource.

Subject classifications