Asymptotic enumeration of two-dimensional posets
It is shown that the number of pairwise nonisomorphic two-dimensional posets with n elements is asymptotically equivalent to \(1/2\;n!\) The estimate is based on the following theorem: For prime two-dimensional posets P there exists a unique unordered pair \(\{L_ 1,L_ 2\}\) of linear extensions of P whose intersection is P. Here a poset P is called prime if there is no subset A of P with the following properties: \(1<| A| <| P|\), for every \(a_ 1,a_ 2\in A\), \(b\in P- A\), \(b<a_ 1\) iff \(b<a_ 2\), \(a_ 1<b\) iff \(a_ 2<b\).
scientific article; zbMATH DE number 4106914
scientific article