A277083 -id:A277083 - cp's OEIS frontend

A277086 Irregular triangle read by rows: T(n,k) = number of size k subsets of S_n with respect to the symmetries of the square.

1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 5, 5, 2, 1, 1, 7, 56, 317, 1524, 5733, 17728, 44767, 94427, 166786, 249624, 316950, 343424, 316950, 249624, 166786, 94427, 44767, 17728, 5733, 1524, 317, 56, 7, 1, 1, 23, 1012, 36125, 1035496, 23878229, 456936220, 7437730463

Offset: 0

Christian Bean, Sep 28 2016

A permutation, p, can be thought of as a set of points (i, p(i)). In this viewpoint it is natural to consider the symmetries of the square.

T(n,k) is the number of symmetry classes of subsets of size k from S_n.

			Triangle starts:
1, 1;
1, 1;
1, 1, 1;
1, 2, 5, 5, 5, 2, 1;

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.

Rows lengths give A038507.

Cf. A277080, A277081, A277083, A277085.

T(n,k) = 1/8 * (C(n,k) + 2*A277080(n,k) + 2*A277081(n,k) + 2*A277085(n,k) + A277083(n,k)).

cp's OEIS Frontend

A277086 Irregular triangle read by rows: T(n,k) = number of size k subsets of S_n with respect to the symmetries of the square.

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