[seqfan] Re: Labeled posets on 8 elements with longest chain 4 or 5

[Brendan McKay]

Hi Richard,  Your counts have the total 431723379 which appears in
A001035 and was computed independently at least twice. I don't
find the counts per height anywhere but I can recompute them.

Brendan.

On 15/3/21 12:08 am, Richard J. Mathar wrote:
> Has anyone a count of the labeled, not necessarily connected posets
> on 8 vertices/elements with longest chain 4 or 5? This refers
> to Comtet's table in section 1.16 of his book, which is reproduced
> in A008285. I get for the 8-th row
> 1 6285806 142259628 199357704 71310960 11481120 987840 40320
> not
> 1 6285806 142259628 199424904 71243760 11481120 987840 40320
> as printed by Comtet. (Erne in 1974 does not mention these....)
> [I do reproduce all values in the first seven rows. The program
> takes McKay's poset table at the bottom of
> http://users.cecs.anu.edu.au/~bdm/data/digraphs.html,
> calculates the order A of the automorphism group of each of the 183231
> posets with V=8 points, and sums over V!/A.]
> In summary: is there any (hopefully published) erratum to the last
> known row of A008285?
>
> Richard
>
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