A242044 Number of isomorphism classes of involutory abelian/medial quandles of order n.

1, 1, 3, 4, 11, 33, 121, 597, 4017, 35103, 428081, 6851591, 153025577, 4535779061, 187380634552

Offset: 1

Author

David Stanovsky, Oct 01 2014

Keywords

• nonn
• hard

Comments

Both names "abelian" and "medial" refer to the identity (xy)(uv)=(xu)(yv). A (left) quandle is involutory (aka symmetric, kei) if all (left) translations have order at most 2, i.e., x(xy)=y is satisfied.

Enumerates intersection of the classes enumerated in A165200, A178432.

Links

• P. Jedlička, A. Pilitowska, D. Stanovský, A. Zamojska-Dzienio, The structure of medial quandles, arXiv:1409.8396 [math.GR], 2014.
• David Stanovský, Calculating with quandles GAP code to calculate the numbers.

Crossrefs

Cf. A165200, A178432.