A212319 The number of abstract groups with minimal permutation representations of degree n.

1, 1, 2, 5, 7, 13, 26, 82, 104, 212, 441, 1171, 1780

Offset

1,3

Comments

a(n) can be derived by setting a(1)=1 and then taking the differences between the consecutive elements of A174511. This is due to the fact that if an abstract group can be represented as a permutation group on n points, then it can also be represented by a permutation group of degree n+1, simply by including a fixed point. In other words, the sum of the first n terms give you the number of isomorphism classes of subgroups of the symmetric group of degree n.

Links

Table of n, a(n) for n=1..13.

Formula

a(1)=1, a(n) = A174511(n) - A174511(n-1), n>1.

Example

a(1)=1, since only the trivial group 1 can be represented as permutations of a single point. a(2)=1 because Z_2,1 can both be realized by permutations of two points but for 1 this representation is not minimal. a(3)=2 with Z_3 and S_3 appearing for the first time.

Crossrefs

Cf. A174511.

Sequence in context: A119839 A360105 A107057 * A161379 A250173 A038945

Adjacent sequences: A212316 A212317 A212318 * A212320 A212321 A212322

Keyword

nonn,more

Author

Attila Egri-Nagy, Oct 25 2013

Status

approved