= Binary initial segments maximize contained square faces
{title2=$f(\mathcal A)\leq f(I_{|\mathcal A|})$}
Among families of a given size in the <Boolean hypercube>, a <binary initial segment> maximizes the number of contained two-dimensional <cube faces>. Under <section compression in binary order>, faces crossing the selected coordinate correspond to internal edges in the intersection of its two sections. The edge extremal theorem and <mathematical induction> control that contribution and the faces within the sections.
Back to article page
