Logarithmically concave sequence: Difference between revisions

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In [[mathematics]], a sequence {{math| ''a''}} = {{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 ≥ ''a''_''i''−1''a''_''i''+1}} holds for {{math|0 < ''i'' < ''n'' }}.

'''Remark:''' some authors (explicitely or not) add two further hypotheses in the definition of log-concaves sequences:

* {{math|''a''}} is non-negative

* {{math|''a''}} has no internal zeros; in other words, the support of {{math|''a''}} is a connected interval of {{math|'''Z'''}}.

For instance, the sequence {{math|(1,1,0,0,1)}} checks the inequalities but not the internal zeros condition.