Title: Hasse diagrams of non-isomorphic posets with $n$ elements, $2\leq n \leq 7,$ and the number of posets with $10$ elements, without the aid of any computer program,
Abstract: Let $P(n)$ be the set of all posets with $n$ elements and $NIP(n)$ the set of
non-isomorphic posets with $n$ elements. Let $P^{(j)}(n)$, $1\leq j\leq 2^n,$
be the number of all posets with $n$ elements possessing exactly $j$
antichains. We have determined the numbers $P^{(j)}(7),$ $1\leq j\leq 128$, and
using a result of M. Erné \cite{EM4}, we compute $|P(10)|$ without the aid of
any computer program. We include the Hasse diagrams of all the non-isomorphic
posets of $P(7)$.