OFFSET
1,2
COMMENTS
Also the number of equivalence classes of n-permutations, where pi and sigma are equivalent iff there is a n-permutation rho whose action on the inversion set of sigma is either an order-preserving or order-reversing bijection onto the set of inversions of pi.
Also the number of non-isomorphic transitively oriented permutations graphs on n vertices, where each transitive orientation is identified with its reverse. - Sally Cockburn, Jul 27 2011
LINKS
Sally Cockburn, The Homomorphism Poset for K_{2,n} arXiv:1008.1736v1 [math.CO]
Sally Cockburn, Python program
Rick Decker, C++ program
EXAMPLE
For n=3, the 4 equivalence classes of 3-permutations 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].
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Sally Cockburn, Sep 07 2010, Sep 08 2010
STATUS
approved