An inequality conjectured by Hajela and Seymour arising in combinatorial geometry
In a recent paper, \textit{D. Hajela} and \textit{P. Seymour} [same journal 5, 205-214 (1985; Zbl 0597.05003)] proved that for \(0\leq b_ 1\leq b_ 2\leq 1\), \(\alpha =(\log_ 2 3)/2\), \[ b_ 1^{\alpha}b_ 2^{\alpha}+(1- b_ 1)^{\alpha}b_ 2^{\alpha}+(1-b_ 1)^{\alpha}(1-b_ 2)^{\alpha}\geq 1, \] and drew from this inequality a variety of interesting results in combinatorial geometry. They also conjectured a generalization of the inequality to n variables, which they showed to imply a lower bound on the number of different sequences obtained when members of n sets of zero-one sequences are added to one another. We prove their conjecture, not easy to verify even for small values of n, using complex-variable theory.
scientific article; zbMATH DE number 4021494