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Logarithmic Concavity and sl2(C)

✍ Scribed by David G. Wagner

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 88 KB
Volume: 94
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.2000.3144

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✦ Synopsis

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 algebra sl 2 (C) from which this logarithmic concavity follows. Thus, in applying this strategy to prove logarithmic concavity, the only issue is to construct such a representation naturally from given combinatorial data. As an example, we do this when a j is the number of j-element stable sets in a claw-free graph, reproving a theorem of Hamidoune.

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