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* Princeton Discrete Math Seminar *
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Speaker: Igor Pak (UCLA)
Thursday 30th March, 3:00 in Fine Hall 224.
Title: Correlation inequalities for linear extensions
In this talk I will give a broad overview of correlation inequalities for
linear extensions of finite posets. I will start by reviewing the
background: Stanley's log-concave inequality, Shepp's XYZ inequality, etc.
I will then proceed to describe two new families of correlation inequalities
which we recently established. The first is motivated by the
Huh–Schröter–Wang correlation inequalities for matroids, and is proved via
the technology of combinatorial atlases. The second is motivated by the
Lam–Pylyavskyy inequalities for Schur functions, and is proved via the
multivariate generalization of the Ahlswede–Daykin inequality. Joint
work with Swee Hong Chan.
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