A181771 Number of isomorphism classes of connected quandles of order n.

1, 0, 1, 1, 3, 2, 5, 3, 8, 1, 9, 10, 11, 0, 7, 9, 15, 12, 17, 10, 9, 0, 21, 42, 34, 0, 65, 13, 27, 24, 29, 17, 11, 0, 15, 73, 35, 0, 13, 33, 39, 26, 41, 9, 45, 0, 45

Offset: 1

Author

James McCarron

Keywords

• nonn
• hard
• more

Comments

It is not clear whether the empty quandle is connected, so the sequence starts at order 1 instead of 0.

References

• Hulpke, A. Personal communication, 2014.
• Holt, D.; Royle, G. Personal communication, 2014.

Links

• John J. Cannon and Derek F. Holt, The transitive permutation groups of degree 32, Experiment. Math. 17 (2008), no. 3, 307--314.
• A. Hulpke, Constructing transitive permutation groups, J. Symbolic Comput. 39 (2005), 1-30.
• J. McCarron, Connected Quandles with Order Equal to Twice an Odd Prime, arXiv preprint arXiv:1210.2150 [math.GR], 2012. - From _N. J. A. Sloane_, Dec 31 2012
• Sam Nelson, Quandles and Racks.
• Leandro Vendramin, On the classification of quandles of low order, arXiv:1105.5341 [math.GT], 2011-2012.
• Leandro Vendramin and Matías Graña, Rig, a GAP package for racks and quandles.

Crossrefs

Cf. A181769, A176077.

Programs

GAP

# (using the Rig package)
LoadPackage("rig");
for n in [1..47] do  Display(NrSmallQuandles(n));  od;
# Leandro Vendramin, Sep 14 2014

Extensions

Ninth term corrected by James McCarron, Dec 05 2010

More terms from Leandro Vendramin, Sep 14 2014