Edge-isoperimetric theorem for binary initial segments
= Edge-isoperimetric theorem for binary initial segments
Among subsets of the $n$-dimensional <hypercube graph> with $a$ vertices, initial segments of the <binary order on the discrete cube> minimize the <edge boundary>. Its exact minimum is $na-2\sum_{j=0}^{a-1}s_2(j)$. This strengthens the entropy lower bound on the same boundary.