cp's OEIS Frontend

A263802 Number of independent sets of permutations of n points, i.e., subsets of the symmetric group of degree n, with the property that none of the elements in the subset can be generated by the rest of the subset.

%I A263802 #15 Dec 14 2015 12:03:33
%S A263802 2,3,16,413,25346,6825268
%N A263802 Number of independent sets of permutations of n points, i.e., subsets of the symmetric group of degree n, with the property that none of the elements in the subset can be generated by the rest of the subset.
%o A263802 (GAP)
%o A263802 # GAP 4.7 http://www.gap-system.org
%o A263802 # brute-force  enumeration of independent sets in the symmetric group
%o A263802 # inefficient (~4GB RAM needed, n=4 can take hours),
%o A263802 # but short, readable, self-contained
%o A263802 # higher terms can be calculated by the SubSemi package
%o A263802 # https://github.com/egri-nagy/subsemi
%o A263802 IsIndependentSet := function(A)
%o A263802 return IsDuplicateFreeList(A) and
%o A263802          (Size(A)<2 or
%o A263802           ForAll(A,x-> not (x in Group(Difference(A,[x])))));
%o A263802 end;
%o A263802 for n in [1..4] do
%o A263802 Sn := SymmetricGroup(IsPermGroup,n);
%o A263802 allsubsets := Combinations(AsList(Sn));
%o A263802 iss := Filtered(allsubsets, IsIndependentSet);
%o A263802 Display(Size(iss));
%o A263802 od;
%K A263802 nonn,hard,more
%O A263802 1,1
%A A263802 _Attila Egri-Nagy_, Oct 27 2015