A382507 Number of half turn symmetric lattice congruences of the weak order on the symmetric group S_n.

1, 2, 3, 16, 66, 13726, 11547029

Offset

1,2

Comments

For all permutations p of {1,2,...,n}, let C(p) be the permutation n+1-p(n),...,n+1-p(1). A lattice congruence of the weak order on S_n is said to be half turn symmetric if for all p ~ q we have C(p) ~ C(q).

Half turn symmetric lattice congruences of the weak order form a sublattice of the lattice of all congruences of the weak order, hence they form a distributive lattice.

Links

Table of n, a(n) for n=1..7.

Example

The lattice congruence of the weak order whose quotient is the lattice of Baxter permutations is half turn symmetric. Lattice congruences giving the Tamari lattice are not half turn symmetric.

Crossrefs

Cf. A091687.

Sequence in context: A052506 A355229 A052858 * A191416 A209004 A329121

Adjacent sequences: A382504 A382505 A382506 * A382508 A382509 A382510

Keyword

nonn,more

Author

Ludovic Schwob, Mar 30 2025

Status

approved