
COMMENTS

Also the number of equivalence classes of npermutations, where pi and sigma are equivalent iff there is a npermutation rho whose action on the inversion set of sigma is either an orderpreserving or orderreversing bijection onto the set of inversions of pi.
Also the number of nonisomorphic transitively oriented permutations graphs on n vertices, where each transitive orientation is identified with its reverse.  Sally Cockburn, Jul 27 2011


EXAMPLE

For n=3, the 4 equivalence classes of 3permutations are:
[123], [132, 213], [231, 312], [321].
For n= 4, the 12 equivalence classes are: [1234], [1243, 1324, 2134], [2143], [1342, 1423, 2314, 3124], [1432, 3214], [2413, 3142], [4123, 2341], [3412], [2431, 4132, 3241, 4213], [4231], [4312, 3421], [4321].
