A366705 Number of symmetry classes of partially ordered pattern classes defined by avoiding a size n poset.
1, 1, 2, 7, 64, 1068, 32651
Offset: 0
Examples
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.
Links
- Christian Bean, Émile Nadeau, Jay Pantone, and Henning Ulfarsson, Permutations avoiding bipartite partially ordered patterns have a regular insertion encoding, The Electronic Journal of Combinatorics, Volume 31, Issue 3 (2024); arXiv preprint, arXiv:2312.07716 [math.CO], 2023.
- Alice L. L. Gao and Sergey Kitaev, On partially ordered patterns of length 4 and 5 in permutations, arXiv:1903.08946 [math.CO], 2019.
- Alice L. L. Gao and Sergey Kitaev, On partially ordered patterns of length 4 and 5 in permutations, The Electronic Journal of Combinatorics 26(3) (2019), P3.26.
Crossrefs
Cf. A001035.