Bounds on maximal families of sets not containing three sets with \(A\cap B \subset C\), \(A \not\subset B\)
Let \(\text{La}^\sharp(n,V_2)\) denote the size of the largest family \(\mathcal{F}\) of subsets of \(\{1,2,\dots,n\}\) containing no three distinct members \(F, G_1, G_2 \in \mathcal{F}\) such that \(F \subset G_1\), \(F \subset G_2\), \(G_1 \not\subset G_2\). The following inequalities are proved in this paper: \[ {n \choose {\lfloor \frac{n}{2} \rfloor}} \left(1 + \frac{1}{n} + \Omega \left(\frac{1}{n^2}\right)\right)\leq\text{La}^\sharp(n,V_2)\leq {n \choose {\lfloor \frac{n}{2} \rfloor}}\left(1 + \frac{2}{n} + O\left(\frac{1}{n^2}\right)\right). \]
scientific article; zbMATH DE number 5366786