%I #23 Jul 22 2024 09:47:41

%S 1,1,2,7,64,1068,32651

%N Number of symmetry classes of partially ordered pattern classes defined by avoiding a size n poset.

%H Christian Bean, Émile Nadeau, Jay Pantone, and Henning Ulfarsson, <a href="https://doi.org/10.37236/12686">Permutations avoiding bipartite partially ordered patterns have a regular insertion encoding</a>, The Electronic Journal of Combinatorics, Volume 31, Issue 3 (2024); <a href="https://arxiv.org/abs/2312.07716">arXiv preprint</a>, arXiv:2312.07716 [math.CO], 2023.

%H Alice L. L. Gao and Sergey Kitaev, <a href="https://arxiv.org/abs/1903.08946">On partially ordered patterns of length 4 and 5 in permutations</a>, arXiv:1903.08946 [math.CO], 2019.

%H Alice L. L. Gao and Sergey Kitaev, <a href="https://doi.org/10.37236/8605">On partially ordered patterns of length 4 and 5 in permutations</a>, The Electronic Journal of Combinatorics 26(3) (2019), P3.26.

%e There are three labeled posets with 2 elements. The two chains generate symmetrically equivalent permutation classes, Av(12) and Av(21), while the third generates Av(12, 21) which is not equivalent to these. Therefore a(2) = 2.

%Y Cf. A001035.

%K nonn,more

%O 0,3

%A _Jay Pantone_, Oct 17 2023