OFFSET
0,2
COMMENTS
By diamond-shaped poset with 4 vertices, we mean a poset on four elements with e_1 < e_2, e_1 < e_3, e_2 < e_4, e_3 < e_4, and no order relations between e_2 and e_3. In the Hasse diagram for such a poset, we have a least element, two elements in the level above, and one element in the top level, so the diagram resembles a diamond.
LINKS
M. Paukner, L. Pepin, M. Riehl, and J. Wieser, Pattern Avoidance in Task-Precedence Posets, arXiv:1511.00080 [math.CO], 2015.
FORMULA
a(n) = (4n)!/12^n.
EXAMPLE
For a single diamond (n=1) poset with 4 vertices, we must label the least element 1 and the greatest element 4, and the two central elements can be labeled either 2, 3 or 3, 2 respectively. Thus the associated permutations are 1234 and 1324.
MATHEMATICA
Table[(4 n)!/12^n, {n, 0, 12}] (* Michael De Vlieger, Apr 06 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Manda Riehl, Jul 29 2015
EXTENSIONS
More terms from Michael De Vlieger, Apr 06 2016
a(4) corrected by Georg Fischer, May 08 2021
STATUS
approved