[seqfan] A022016 and A022017 (was Re: Looking back at your earliest sequences)

[Robert Munafo]

On 3/15/13, franktaw at netscape.net <franktaw at netscape.net> wrote:
> It appears my first sequences were A022016 and A02207. I'm actually
> rather disappointed that no one has done anything with them.

Okay, I'll ask. Can you add explicit well-explained examples to
A022016 and A022017?

A022016 calls itself:

  "Partially ordered sets with no isolated points by number of
"lines": pairs (a,b) where a < b and there is no c with a < c < b. The
lines form the minimal basis for the partial ordering."

and it begins 1, 1, 4, 12, 47, ...

So A022016[2] = 4, that must mean there are 4 partially-ordered sets
that have something in common. Does their common property have
something to do with 2? Are they sets of integers, or sets of sets of
integers, or sets of points? Can you actually list the 4 sets giving
all their elements? Your use of the word "lines" evokes geometric
imagery. Why call them "lines"? (What is linear about them?)

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