A260331 - OEIS

%I #37 Nov 05 2025 15:22:29

%S 1,2,280,277200,1009008000,9777287520000,207786914375040000,

%T 8508874143657888000000,611958228411875304960000000,

%U 72094798889203029677337600000000,13177487340968529764423766528000000000,3577714168047637768100581459885056000000000,1392303245637418713834022280928868392960000000000

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

%C 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.

%H M. Paukner, L. Pepin, M. Riehl, and J. Wieser, <a href="https://arxiv.org/abs/1511.00080">Pattern Avoidance in Task-Precedence Posets</a>, arXiv:1511.00080 [math.CO], 2015.

%H Manda Riehl, <a href="/A260331/a260331.png">A labelling of a diamond with 4 vertices so that the labels follow the poset relations.</a>

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

%e 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.

%t Table[(4 n)!/12^n, {n, 0, 12}] (* _Michael De Vlieger_, Apr 06 2016 *)

%Y Cf. A260332, A260579.

%K nonn

%O 0,2

%A _Manda Riehl_, Jul 29 2015

%E More terms from _Michael De Vlieger_, Apr 06 2016

%E a(4) corrected by _Georg Fischer_, May 08 2021