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

Author

Ludovic Schwob, Mar 30 2025

Keywords

• nonn
• more

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.

Examples

			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.