A243931 Number of isomorphism classes of 2-reductive involutory abelian/medial quandles.

1, 1, 2, 4, 10, 31, 120, 594, 4013, 35092, 428080, 6851545, 153025576, 4535778875, 187380634539, 10385121165057, 801710433900516

Offset

1,3

Comments

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

Links

Table of n, a(n) for n = 1..17

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. A242044, A242275.

Sequence in context: A242347 A138415 A005268 * A005269 A070900 A296003

Adjacent sequences: A243928 A243929 A243930 * A243932 A243933 A243934

Keyword

nonn,hard

Author

David Stanovsky, Oct 01 2014

Status

approved