This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A382507 #4 Apr 04 2025 22:46:08
%S A382507 1,2,3,16,66,13726,11547029
%N A382507 Number of half turn symmetric lattice congruences of the weak order on the symmetric group S_n.
%C A382507 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).
%C A382507 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.
%e A382507 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.
%Y A382507 Cf. A091687.
%K A382507 nonn,more
%O A382507 1,2
%A A382507 _Ludovic Schwob_, Mar 30 2025