A q-analogue of the FKG inequality and some applications

Let L be a finite distributive lattice and µ : L → R+ a logsupermodular function. For functions k : L → R+ let Eµ(k; q) def = x∈L k(x)µ(x)qrank(x) ∈ R+ [q]. We prove for any pair g, h : L → R+ of monotonely increasing functions, that Eµ(g; q) · Eµ(h; q) Eµ(1; q) · Eµ(gh; q), where “ ” denotes coefficientwise inequality of real polynomials. The FKG inequality of Fortuin, Kasteleyn and Ginibre (1971) is the real number in

• Type: Journal
• Year: 2011
• Where: COMBINATORICA
• Authors: Anders Björner
• Keywords: COMBINATORICA 2011, Distributive Lattice, Fkg Inequality, Fortuin, Optimization