A330039
Number of essential lattice congruences of the weak order on the symmetric group S_n.
Original entry on oeis.org
1, 1, 4, 47, 3322, 11396000
Offset: 1
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}.
- 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.
A330040
Number of non-isomorphic cover graphs of lattice quotients of essential lattice congruences of the weak order on the symmetric group S_n.
Original entry on oeis.org
1, 1, 3, 19, 748, 2027309
Offset: 1
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 graphs, showing that a(3)=3.
- 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.
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.
Original entry on oeis.org
1, 1, 3, 10, 51, 335, 2909
Offset: 1
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.
- 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.
A091688
Number of lattice congruences of the weak order on the Coxeter group B_n.
Original entry on oeis.org
1, 2, 19, 8368, 360350697981
Offset: 0
Nathan Reading (nreading(AT)umich.edu), Jan 28 2004
A382507
Number of half turn symmetric lattice congruences of the weak order on the symmetric group S_n.
Original entry on oeis.org
1, 2, 3, 16, 66, 13726, 11547029
Offset: 1
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.
Showing 1-5 of 5 results.
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