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a(n) is the number of non-isomorphic geometric realizations (rectilinear drawings) of K_{2,n}.
1

%I #11 Mar 31 2012 10:30:45

%S 1,2,4,12,39,182,1033,7605,66302

%N a(n) is the number of non-isomorphic geometric realizations (rectilinear drawings) of K_{2,n}.

%C 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.

%C 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

%H Sally Cockburn, <a href="http://arxiv.org/abs/1008.1736">The Homomorphism Poset for K_{2,n}</a> arXiv:1008.1736v1 [math.CO]

%H Sally Cockburn, <a href="/A180487/a180487.txt">Python program</a>

%H Rick Decker, <a href="/A180487/a180487a.txt">C++ program</a>

%e For n=3, the 4 equivalence classes of 3-permutations are:

%e [123], [132, 213], [231, 312], [321].

%e 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].

%K nonn,hard,more

%O 1,2

%A _Sally Cockburn_, Sep 07 2010, Sep 08 2010