This is a list of libraries of algebraic structures that I have generated, usually accompanying a paper.

Racks and quandles of small orders [Experimental. Last update 7/30/2018]

Download: zip file (19 MB, unpacks to 200MB)

Instructions: unzip the file and read instructions in the file "library_of_racks_and_quandles.gi".

The library contains:

• all racks of order ≤ 11 up to isomorphism,
• all quandles of order ≤ 12 up to isomorphism,
• all non-2-reductive racks of orders 12, 13 up to isomorphism, and
• all non-2-reductive quandles of order 13 up to isomorphism.

Let r(n), resp. q(n), denote the number of racks, resp. quandles, of order n up to isomorphism. Then:

n	1	2	3	4	5	6	7
r(n)	1	2	6	19	74	353	2080
q(n)	1	1	3	7	22	73	298
n	8	9	10	11	12	13	14
r(n)	16023	159526	2093244	36265070	836395102	25794670618	?
q(n)	1581	11079	102771	1275419	21101335	469250886	?

Let r*(n), resp. q*(n), denote the number or non-2-reductive racks, resp. non-2-reductive quandles, of order n up to isomorphism. Then:

n	1	2	3	4	5	6	7
r*(n)	0	0	1	2	9	30	120
q*(n)	0	0	1	2	7	18	52
n	8	9	10	11	12	13	14
r*(n)	602	3637	28556	282713	3697095	63619757	?
q*(n)	183	778	4239	28940	264164	3163262	?

A rack or quandle is 2-reductive if and only if its left translations generate an abelian group, otherwise it is non-2-reductive.