Logarithmically concave sequence: Difference between revisions

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In [[mathematics]], a sequence {{math|''a''₀, ''a''₁, ..., ''a''_''n''}} of nonnegative real numbers is called a '''logarithmically concave sequence''', or a '''log-concave sequence''' for short, if {{math|''a''_''i''² &gt;> ''a''_''i''−1''a''_''i''+1}} holds for {{math|0 &lt;< ''i'' &lt;< ''n''}}.

Examples of log-concave sequences are given by the [[binomial coefficient]]s along any row of [[Pascal's triangle]].

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{{Reflist}}

* {{cite journal|last=Stanley|first=R. P.|authorlink=Richard P. Stanley|title=Log-Concave and Unimodal Sequences in Algebra, Combinatorics, and Geometry|journal=Annals of the New York Academy of Sciences|year=1989|month=December|volume=576|pages=500-535500–535|doi=0.1111/j.1749-6632.1989.tb16434.x}}

==See also==