The dimension of interior levels of the Boolean lattice. II (Q1970928)

[For part I see ibid. 11, No. 1, 29-40 (1994; Zbl 0809.06004).] The authors establish the dimension \(d(3,m;n)\) of the containment order generated by the 3-element and \(m\)-element subsets of an \(n\)-element set for most \(m\) between \(2\sqrt{n}\) and \(n\). Main results: 1. Let \(n,m\) and \(t\) be positive integers, \(n> 2t+4\) and \(m>t+ \frac{n+1}{t+1}\). Then \(d(3,m;n)\geq n-t-1\). 2. If \(n> t^2+1\) and \(m\leq t-2+ \frac{n-1}{t}\) then \(d(3,m;n)\leq n-t-1\).