A327150
Number of orbits of the direct square of the alternating group A_n^2 where A_n acts by conjugation.
Original entry on oeis.org
1, 1, 1, 9, 22, 77, 400, 2624, 20747, 183544, 1826374, 20045348, 240262047, 3120641718, 43665293393, 654731266933, 10472819759734, 178001257647196, 3203520381407270, 60859480965537820, 1217072840308660049
Offset: 0
For n = 3, representatives of the n=9 orbits are (e,e), (e,(123)), (e,(132)), ((123),e), ((132),e), ((123),(123)), ((123),(132)), ((132),(123)), ((132),(132)), where e is the identity.
A327015
Number of equivalence classes of pairs of permutations in S_n where two pairs are equivalent if they are simultaneously conjugate to each other or simultaneously conjugate to each other after a reversal of one pair.
Original entry on oeis.org
1, 1, 3, 8, 28, 98, 518, 3096, 23415, 201795, 1973189, 21347935, 253282652, 3263902430
Offset: 0
For n = 2, representatives of the a(2) = 3 classes are: (e,e), (e, (12)), ((12),(12)), where e is identity.
A327151
Number of orbits of the direct square of the alternating group A_n^2 where A_n acts by conjugation, such that both permutations in a representative pair are of the same conjugacy class in A_n.
Original entry on oeis.org
1, 1, 1, 3, 8, 23, 82, 452, 2369, 18356, 143308, 1396222, 13000455, 152886068
Offset: 0
For n = 3, representatives of the a(3) = 3 orbits are: (e,e), ((123),(123)), ((132),(132)), where e is the identity.
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