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

[Antti Karttunen]

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