Pairwise intersections and forbidden configurations (Q850074)

This interesting paper proves at first a strong stability version of the celebrated complete intersection theorem of Ahlswede and Khachatrian in the spirit of the Hilton-Milner theorem. Then using it the authors prove the following result: let \(f_m(a,b,c,d)\) denote the maximum size of a family of an \(m\)-element underlying set with the property that for all pairs \(A,B\) we have \(| A \cap B| \geq a,\) \(| \overline{A} \cap B| \geq b,\) \(| A \cap \overline{B}| \geq c\) and \(| \overline{A} \cap \overline{B}| \geq d.\) Then \(f_m(a,b,c,d) = \Theta( m^{a+b-1})\) for a wide range of the parameters.