[seqfan] Re: An interesting graph/lattice structure in A333123.

[Ali Sada]

 Hi Antti,
Thank you very much for this amazing work. The graph and the two sequences you created are beautiful!
A333123 is entirely the work of Dr. Wilson. He was generous to add my name as co-author. And I am not an expert on math naming, but if it was lattice and it was my decision to chose the name I would call it the Wilson-Lattice or the Wilson-Karttunen Lattice.
Thank you again and again!
Best,
Ali

    On Sunday, April 5, 2020, 10:03:04 PM EDT, Antti Karttunen <antti.karttunen at gmail.com> wrote:  
 
 Cheers all,

Inspired by a recent nice sequence from Ali Sada & Bob Wilson, I
started computing a few of the derived sequences from the lattice (or
graph) inherently present. See e.g.,

https://oeis.org/history/view?seq=A333123&v=44

and for example:

https://oeis.org/draft/A332992 ("outdegree" because we think the edge
direction to be towards 1)
and
https://oeis.org/draft/A332999 ("indegree" for ditto)

Now I wonder, what would be a good terminology to use here, from the
graph or order theory? For now I'm hopelessly mixing them, and in any
case, I always mix my meets and joins.

Furthermore, is it really a lattice, in the sense of
https://en.wikipedia.org/wiki/Lattice_(order)
?

And is it not something already known in "the literature", how we
should call it? ("Sada-Wilson Lattice" ?)

Also, there are many other things that could be computed for each such
finite lattice (with max. element n), e.g., the size of maximal
antichain, and so on.


Best regards,

Antti

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