A330042 Number of non-isomorphic regular cover graphs of lattice quotients of essential lattice congruences of the weak order on the symmetric group S_n.

1, 1, 3, 10, 51, 335, 2909

Offset

1,3

Links

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

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.

Example

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 four essential lattice congruences, namely {}, {132=312}, {213=231}, {132=312,213=231}. The cover graph of the first one is a 6-cycle, the cover graph of the middle two is a 5-cycle, and the cover graph of the last one is a 4-cycle. These are 3 non-isomorphic regular graphs, showing that a(3)=3.

Crossrefs

Cf. A091687, A001246, A052528, A024786, A123663, A330039, A330040.

Sequence in context: A192482 A233537 A020132 * A241459 A350895 A230740

Adjacent sequences: A330039 A330040 A330041 * A330043 A330044 A330045

Keyword

nonn,hard

Author

Torsten Muetze, Nov 28 2019

Status

approved