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%I #11 Jun 22 2020 06:56:31
%S 1,1,3,10,51,335,2909
%N Number of non-isomorphic regular cover graphs of lattice quotients of essential lattice congruences of the weak order on the symmetric group S_n.
%H Hung Phuc Hoang, Torsten Mütze, <a href="https://arxiv.org/abs/1911.12078">Combinatorial generation via permutation languages. II. Lattice congruences</a>, arXiv:1911.12078 [math.CO], 2019.
%H V. Pilaud and F. Santos, <a href="https://arxiv.org/abs/1711.05353">Quotientopes</a>, arXiv:1711.05353 [math.CO], 2017-2019; Bull. Lond. Math. Soc., 51 (2019), no. 3, 406-420.
%e 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.
%Y Cf. A091687, A001246, A052528, A024786, A123663, A330039, A330040.
%K nonn,hard
%O 1,3
%A _Torsten Muetze_, Nov 28 2019