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

1,5

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

Table of n, a(n) for n=1..47.

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.

Prog

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

Crossrefs

Cf. A181769, A176077.

Sequence in context: A086670 A075888 A075889 * A238628 A045766 A281668

Adjacent sequences: A181768 A181769 A181770 * A181772 A181773 A181774

Keyword

nonn,hard,more

Author

James McCarron

Extensions

Ninth term corrected by James McCarron, Dec 05 2010

More terms from Leandro Vendramin, Sep 14 2014

Status

approved