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

[Neil Sloane]

Concerning A022016, A022017, I will add drawings of some small examples.
Neil

On Sun, Mar 17, 2013 at 1:48 AM, Robert Munafo <mrob27 at gmail.com> wrote:

> 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?)
>
> --
>   Robert Munafo  --  mrob.com
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-- 
Dear Friends, I have now retired from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA
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Email: njasloane at gmail.com