Logarithmic concavity and sI(2)(C)

We observe that for any logarithmically concave finite sequence a(0), a(1), .... a(n) of positive integers there is a representation of the Lie algebr a sl(2)(C) from which this logarithmic concavity follows. Thus, in applying this strategy to prove logarithmic concavity. the only issue is to constru ct such a representation naturally from given combinatorial data. As an exa mple, we do this when cr, is the number of j-element stable sets in a claw- free graph. reproving a theorem of Hamidoune. (C) 2001 Academic Press.