Correlation inequalities for Schur positivity

We generalize the Ahlswede–Daykin inequality (1978) to a Schur positive \emph{ADS inequality}, which also contains the Lam–Postnikov–Pylyavskyy inequality (2007) as a special case. We then present a number of further generalizations and applications. Notably, we resolve Mihalcea’s conjecture on log-supermodularity of stable Grothendieck polynomials.