Hasse diagrams of posets with up to 7 elements, and the number of posets with 10 elements, without the use of computer programs

Luiz F. Monteiro, Sonia Savini, Ignacio Viglizzo

Let $P(n)$ be the set of all posets with $n$ elements. Let $P^{(j)}(n)$, $1\le j\le 2^n,$ be the number of all posets with $n$ elements possessing exactly $j$ antichains. We have…