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In [[mathematics]], a sequence {{math|''a''}} = {{math| (''a''<sub>0</sub>, ''a''<sub>1</sub>, ..., ''a''<sub>''n''</sub>)}} of nonnegative real numbers is called a '''logarithmically concave sequence''', or a '''log-concave sequence''' for short, if {{math|''a''<sub>''i''</sub><sup>2</sup> ≥ ''a''<sub>''i''−1</sub>''a''<sub>''i''+1</sub>}} holds for {{math|0 < ''i'' < ''n'' }}.
'''Remark:''' some authors (explicitely or not) add two further hypotheses in the definition of log-
* {{math|''a''}} is non-negative
* {{math|''a''}} has no internal zeros; in other words, the support of {{math|''a''}} is
These hypotheses mirror the ones required for [[Logarithmically_concave_function|log-concave functions]].
For instance, the sequence {{math|(1,1,0,0,1)}} checks the inequalities but not the internal zeros condition.▼
Sequences that fulfill the three conditions are also called '''Pòlya Frequency sequences of order 2''' ('''PF<sub>2</sub>''' sequences). Refer to chapter 2 of <ref name="brenti">Brenti, F. (1989). Unimodal Log-Concave and Pòlya Frequency Sequences in Combinatorics. American Mathematical Society.</ref> for a discussion on the two notions.
▲For instance, the sequence {{math|(1,1,0,0,1)}} checks the concavity inequalities but not the internal zeros condition.
Examples of log-concave sequences are given by the [[binomial coefficient]]s along any row of [[Pascal's triangle]].
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