

A237036


Size of the smallest conjugacy class of size greater than 1 of the alternating group of degree n.


0



3, 12, 40, 70, 105, 168, 240, 330, 440, 572, 728, 910, 1120, 1360, 1632, 1938, 2280, 2660, 3080, 3542, 4048, 4600, 5200, 5850, 6552, 7308, 8120, 8990, 9920, 10912, 11968, 13090, 14280, 15540, 16872, 18278, 19760, 21320, 22960, 24682, 26488, 28380, 30360, 32430
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OFFSET

4,1


LINKS



FORMULA

G.f.: x^4*(7*x^828*x^7+42*x^620*x^520*x^4+30*x^310*x^23)/(x1)^4.
a(n) = 2*C(n,3) = A007290(n) for n>=9. (End)


EXAMPLE

For n = 4 the conjugacy classes of size greater than 1 of Alt(n) are
{(1,2)(3,4), (1,3)(2,4), (1,4)(2,3)},
{(2,4,3), (1,2,3), (1,3,4), (1,4,2)},
{(2,3,4), (1,2,4), (1,3,2), (1,4,3)},
the smallest of which has 3 elements, hence a(4) = 3.


MATHEMATICA

Join[{3, 12, 40, 70, 105}, 2*Binomial[Range[9, 50], 3]] (* Harvey P. Dale, Apr 07 2018 *)


PROG

(GAP)
a:=function(n)
local G, CC, SCC, SCC1;
G:=AlternatingGroup(n);
CC:=ConjugacyClasses(G);;
SCC:=List(CC, Size);
SCC1:=Difference(SCC, [1]);
return Minimum(SCC1);
end;;


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



