Linear extensions of semiorders. II (Q1583842)

Let \(M_{n}( k) \) denote the family of partially ordered sets on \(n\geq 3\) points with exactly \(k\) ordered pairs, \(0\leq k\leq \binom{n}{k}\), that maximize the number of linear extension among all such posets. In part I [\textit{P. C. Fishburn} and \textit{W. T. Trotter}, Discrete Math. 103, 25-40 (1992; Zbl 0758.06002)] it was proved that every poset in \(M_{n}( k) \) is a semiorder and all semiorders in \(M_{n}( k) \) for \(k\leq n\) were identified. In this paper the authors specify \(M_{n}( k) \) for all \(k\leq 2n-3\).