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

Richard J. Mathar mathar at mpia-hd.mpg.de
Sun Mar 14 14:08:59 CET 2021


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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