Correlation inequalities for linear extensions

Igor Pak, UCLA
Fine Hall 224

In-Person Talk 

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. 

This is joint work with Swee Hong Chan.