Abstract
We find an explicit formula for the number of graded partially ordered sets of rank h that can be defined on a set containing n elements. Also, we find the number of graded partially ordered sets of length h, and having a greatest and least element that can be defined on a set containing n elements. The first result provides a lower bound for G*(n), the number of posets that can be defined on an n-set; the second result provides an upper bound for the number of lattices satisfying the Jordan-Dedekind chain condition that can be defined on an n-set.
| Original language | English |
|---|---|
| Pages (from-to) | 12-19 |
| Number of pages | 8 |
| Journal | Journal of Combinatorial Theory |
| Volume | 6 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1969 |