|
|
A177886
|
|
The number of isomorphism classes of Latin quandles (a.k.a. left distributive quasigroups) of order n.
|
|
1
|
|
|
1, 0, 1, 1, 3, 0, 5, 2, 8, 0, 9, 1, 11, 0, 5, 9, 15, 0, 17, 3, 7, 0, 21, 2, 34, 0, 62, 7, 27, 0, 29, 8, 11, 0, 15, 9, 35, 0, 13, 6, 39, 0, 41, 9, 36, 0, 45
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,5
|
|
COMMENTS
|
A quandle is Latin if its multiplication table is a Latin square. A Latin quandle may be described as a left (or right) distributive quasigroup. Sherman Stein (see reference below) proved that a left distributive quasigroup of order n exists if and only if n is not of the form 4k + 2.
|
|
LINKS
|
|
|
EXAMPLE
|
a(2) = 0 since the only quandle of order 2 has multiplication table with rows [1,1] and [2,2].
|
|
PROG
|
(GAP) (using the Rig package)
LoadPackage("rig");
a:=[1, 0];;
Print(1, ", ");
Print(0, ", ");
for n in [3..35] do
a[n]:=0;
for i in [1..NrSmallQuandles(n)] do
if IsLatin(SmallQuandle(n, i)) then
a[n]:=a[n]+1;
fi;
od;
Print(a[n], ", ");
|
|
CROSSREFS
|
See also Index to OEIS under quandles.
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Added fact due to S. K. Stein that a(4k+2) = 0 and a reference to Stein's paper.
|
|
STATUS
|
approved
|
|
|
|