A330039 Number of essential lattice congruences of the weak order on the symmetric group S_n.

1, 1, 4, 47, 3322, 11396000

Offset: 1

Author

Torsten Muetze, Nov 28 2019

Keywords

• nonn
• hard
• more

Examples

			For n=3, the weak order on S_3 has the cover relations 123<132, 123<213, 132<312, 213<231, 312<321, 231<321, and there are a(3)=4 essential lattice congruences, namely {}, {132=312}, {213=231}, {132=312,213=231}.
		

Links

• Hung Phuc Hoang, Torsten Mütze, Combinatorial generation via permutation languages. II. Lattice congruences, arXiv:1911.12078 [math.CO], 2019.
• V. Pilaud and F. Santos, Quotientopes, arXiv:1711.05353 [math.CO], 2017-2019; Bull. Lond. Math. Soc., 51 (2019), no. 3, 406-420.

Crossrefs

Cf. A091687, A001246, A052528, A024786, A123663, A330040, A330042.