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

0,3

Links

Table of n, a(n) for n=0..6.

Christian Bean, Émile Nadeau, Jay Pantone, and Henning Ulfarsson, Permutations avoiding bipartite partially ordered patterns have a regular insertion encoding, 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.

Example

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.

Crossrefs

Cf. A001035.

Sequence in context: A006506 A346781 A011821 * A117263 A046855 A179043

Adjacent sequences: A366702 A366703 A366704 * A366706 A366707 A366708

Keyword

nonn,more

Author

Jay Pantone, Oct 17 2023

Status

approved