A180487 a(n) is the number of non-isomorphic geometric realizations (rectilinear drawings) of K_{2,n}.

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

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

Table of n, a(n) for n=1..9.

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

Sequence in context: A213058 A268069 A215071 * A000940 A008404 A170815

Adjacent sequences: A180484 A180485 A180486 * A180488 A180489 A180490

Keyword

nonn,hard,more

Author

Sally Cockburn, Sep 07 2010, Sep 08 2010

Status

approved