1,2

If f is a permutation of A and g is a permutation of B, the direct product of f and g is the permutation of AXB that maps (a, b) to (f(a), g(b)). The cycle type of the direct product is determined by the cycle types of f and g. - David Wasserman

I will use the notation (i, j, k, ...) for a permutation with i 1-cycles, j 2-cycles, k 3-cycles, etc. and * for direct product. There are 3 cycle types of 3-element permutations: (3), (1, 1) and (0, 0, 1). (3)*(3) has cycle type (9); (3)*(1, 1) has cycle type (3, 3); (3)*(0, 0, 1) has cycle type (0, 0, 3); (1, 1)*(1, 1) has cycle type (4, 1); (1, 1)*(0, 0, 1) has cycle type (0, 0, 1, 0, 0, 1); (0, 0, 1)*(0, 0, 1) has cycle type (0, 0, 3). Since there are 5 distinct answers, a(3) = 5. - David Wasserman

A000041 gives the number of cycle types of an n-element permutation.

Sequence in context: A002094 A115725 A079572 this_sequence A032099 A120896 A074801

Adjacent sequences: A053388 A053389 A053390 this_sequence A053392 A053393 A053394

more,nonn

Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 06 2000

More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Mar 01 2002