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

0,2

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

Table of n, a(n) for n=0..12.

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.

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

Cf. A260332, A260579.

Sequence in context: A172374 A231041 A080296 * A307470 A182519 A279450

Adjacent sequences: A260328 A260329 A260330 * A260332 A260333 A260334

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