A set coverage problem

This paper shows that with B={1,2,...,n}, the smallest k such that(BxB)-{(j,j)|j@?B}=@?i=1k(C"ixD"i) is s(n), where s(n) is the smallest integer k such that n=<(k@?k2@?). This provides a simple set-based formulation and a new proof of a result for boolean ranks (de Caen et al., 1981 [2]) and biclique covering of bipartite graphs (Berukov et al., 2008 [1]; Froncek et al., 2007 [5]), making these intricate results more accessible.