OFFSET
1,3
COMMENTS
Nelson enumerated Alexander quandles to order 16 (see the links below). The values of a(n) for n from 1 to 255 were obtained via a GAP program using ideas from Hou (see the link below).
LINKS
W. Edwin Clark, Table of n, a(n) for n = 1..255
W. E. Clark, M. Elhamdadi, M. Saito and T. Yeatman, Quandle Colorings of Knots and Applications, arXiv preprint arXiv:1312.3307 [math.GT], 2013-2014.
M. Elhamdadi, Distributivity in Quandles and Quasigroups, arXiv preprint arXiv:1209.6518 [math.RA], 2012. - From N. J. A. Sloane, Dec 29 2012
Xiang-dong Hou, Finite Modules over Z[t,t^{-1}], arXiv:1107.2076 [math.RA], 2011.
S. Nelson, Classification of Finite Alexander Quandles, arXiv:math/0202281 [math.GT], 2002-2003.
S. Nelson, Alexander Quandles of Order 16s, arXiv:math/0409460 [math.GT], 2004-2006.
Wikipedia, Racks and Quandles
PROG
(GAP)
findY:=function(f, g)
local Y, y;
Y:=[];
for y in g do
Add(Y, Image(f, y^(-1))*y);
od;
Y:=Set(Y);
return Subgroup(g, Y);
end;;
Alex:=[];; k:=8;;
for nn in [1..2^k-1] do
Alex[nn]:=0;
od;
for n in [1..2^k-1] do
LGn:=AllSmallGroups(n, IsAbelian);
for g in LGn do
autg:=AutomorphismGroup(g);;
eautg:=List(ConjugacyClasses(autg), Representative);
for f in eautg do
N2:=findY(f, g);
MM:= ((Size(g)^2)/Size(N2));
for nn in [1..2^k-1] do
if nn mod MM = 0 then
Alex[nn]:=Alex[nn]+1;
fi;
od;
od;
od;
od;
for nn in [1..2^k-1] do
Print(Alex[nn], ", ");
od;;
CROSSREFS
KEYWORD
nonn
AUTHOR
W. Edwin Clark, Jul 15 2011
STATUS
approved
