A260331 Labelings of n diamond-shaped posets with 4 vertices per diamond where the labels follow the poset relations.

1, 2, 280, 277200, 1009008000, 9777287520000, 207786914375040000, 8508874143657888000000, 611958228411875304960000000, 72094798889203029677337600000000, 13177487340968529764423766528000000000, 3577714168047637768100581459885056000000000, 1392303245637418713834022280928868392960000000000

Offset: 0

Author

Manda Riehl, Jul 29 2015

Keywords

• nonn

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.

Examples

			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.
		

Links

• M. Paukner, L. Pepin, M. Riehl, and J. Wieser, Pattern Avoidance in Task-Precedence Posets, arXiv:1511.00080 [math.CO], 2015.
• Manda Riehl, A labelling of a diamond with 4 vertices so that the labels follow the poset relations.

Crossrefs

Cf. A260332, A260579.

Programs

Mathematica

Table[(4 n)!/12^n, {n, 0, 12}] (* Michael De Vlieger, Apr 06 2016 *)

Formula

a(n) = (4n)!/12^n.

Extensions

More terms from Michael De Vlieger, Apr 06 2016

a(4) corrected by Georg Fischer, May 08 2021