A q-ANALOGUE OF THE FKG INEQUALITY AND SOME APPLICATIONS

(gh;q),where “≪” denotes coefficientwise inequality of real polynomials. The FKGinequality of Fortuin, Kasteleyn and Ginibre (1971) is the real number in-equality obtained by specializing to q = 1.The polynomial FKG inequality has applications to f-vectors of joins andintersections of simplicial complexes, to Betti numbers of intersections of cer-tain Schubert varieties, and to the following kind of correlation inequality forpower series weighted by Young tableaux.Let Y be the set of all integer partitions. Given functions k,µ : Y → R