Now that I think about it, I have used Sage to construct the catalogue of 3-connected binary matroids up to 15 elements. I also get 37 matroids with rank 5 and size 11...
On Wed, Apr 1, 2015 at 8:41 PM, Gordon <[email protected]> wrote: > In a comment to Dillon's latest matroidunion blog post, Sandra Kingan said > "The 3-connected rank 5 and 11 element matroids are only 32 in number" and > then later in the same comment that only 20 do not have an AG(3,2)-minor > > Even assuming that she means "binary matroids" I cannot make my numbers > match hers. > > Here is an array of 37 BinaryMatroids. I believe that > > - they each have rank 5 and size 11 > - they are all 3-connected (at least) > - they are pairwise non-isomorphic > - 24 of them do NOT have an AG(3,2)-minor > - 13 of them do have an AG(3,2) minor and > > Could anyone here confirm that I am not losing my mind (more than usual) and > that these assertions are true? > > Thanks > > Gordon > > mats = [ > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,0,1,1,1], > [0,0,0,0,0,0,1,1,0,0,1], > [0,0,0,1,1,1,0,0,0,0,0], > [0,1,1,0,0,1,0,0,0,0,1], > [1,0,1,0,1,0,0,1,0,1,0]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,0,1,1,1], > [0,0,0,0,0,0,1,1,0,0,1], > [0,0,0,1,1,1,0,0,0,1,0], > [0,1,1,0,0,1,0,0,0,1,1], > [1,0,1,0,1,0,0,1,0,0,0]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,0,1,1,1], > [0,0,0,0,0,0,1,1,0,0,1], > [0,0,0,1,1,1,0,0,0,1,0], > [0,1,1,0,0,1,0,0,0,1,1], > [1,0,1,0,1,0,0,1,0,1,0]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,0,1,1,1], > [0,0,0,0,0,0,1,1,0,0,1], > [0,0,0,1,1,1,0,0,0,0,0], > [0,1,1,0,0,1,0,0,0,1,0], > [1,0,1,0,1,0,0,1,0,0,0]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,0,1,1,1], > [0,0,0,0,0,0,1,1,0,0,1], > [0,0,0,1,1,1,0,0,0,1,0], > [0,1,1,0,0,1,0,0,0,1,0], > [1,0,1,0,1,0,0,1,0,0,0]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,0,1,1,1], > [0,0,0,0,0,0,1,1,0,0,1], > [0,0,0,1,1,1,0,0,0,1,0], > [0,1,1,0,0,1,0,0,0,1,0], > [1,0,1,0,1,0,0,1,0,1,0]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,0,1,1,1], > [0,0,0,0,0,0,1,1,0,0,1], > [0,0,0,1,1,1,0,1,0,1,0], > [0,1,1,0,0,1,0,1,0,1,0], > [1,0,1,0,1,0,0,1,0,1,1]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,0,1,1,1], > [0,0,0,0,0,0,1,1,0,0,1], > [0,0,0,1,1,1,0,0,0,0,1], > [0,1,1,0,0,1,0,0,0,0,1], > [1,0,1,0,1,0,0,1,0,1,1]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,0,1,1,1], > [0,0,0,0,0,1,1,1,0,0,1], > [0,0,0,1,1,0,0,1,0,1,1], > [0,1,1,0,0,0,1,0,0,1,1], > [1,0,1,0,1,0,0,0,0,0,1]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,0,1,1,1], > [0,0,0,0,0,0,1,1,0,0,1], > [0,0,0,1,1,1,0,1,0,1,0], > [0,1,1,0,0,1,0,0,0,0,1], > [1,0,1,0,1,0,0,0,0,1,0]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,0,1,1,1], > [0,0,0,0,0,1,1,1,0,0,0], > [0,0,0,1,1,0,0,1,0,0,1], > [0,1,1,0,0,0,1,0,0,1,0], > [1,0,1,0,1,0,0,0,0,1,1]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,0,1,1,1], > [0,0,0,0,0,1,1,1,0,0,1], > [0,0,0,1,1,0,0,1,0,1,0], > [0,1,1,0,0,0,1,0,0,0,1], > [1,0,1,0,1,0,0,0,0,1,0]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,0,1,1,1], > [0,0,0,0,0,1,1,1,0,0,1], > [0,0,0,1,1,0,0,1,0,1,0], > [0,1,1,0,0,0,1,0,0,0,1], > [1,0,1,0,1,0,0,0,0,1,1]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,1,1,1,1], > [0,0,0,0,0,1,1,0,0,1,1], > [0,0,0,1,1,0,1,0,1,0,0], > [0,1,1,0,0,0,0,0,0,1,1], > [1,0,1,0,1,0,0,0,1,0,1]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,0,1,1,1], > [0,0,0,0,0,1,1,1,0,0,1], > [0,0,0,1,1,0,0,1,0,1,0], > [0,1,1,0,0,0,1,0,0,1,1], > [1,0,1,0,1,0,1,0,0,1,0]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,1,1,1,1], > [0,0,0,0,0,1,1,0,0,1,1], > [0,0,0,1,1,0,1,0,1,0,1], > [0,1,1,0,0,0,0,0,1,1,0], > [1,0,1,0,1,0,0,0,1,0,1]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,0,1,1,1], > [0,0,0,0,0,1,1,1,0,0,0], > [0,0,0,1,1,0,0,1,0,0,1], > [0,1,1,0,1,0,0,0,0,0,0], > [1,0,1,0,0,0,1,0,0,1,0]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,0,1,1,1], > [0,0,0,0,0,1,1,1,0,0,1], > [0,0,0,1,1,0,0,1,0,0,0], > [0,1,1,0,1,0,0,0,0,0,1], > [1,0,1,0,0,0,1,0,0,1,0]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,0,1,1,1], > [0,0,0,0,0,1,1,1,0,0,1], > [0,0,0,1,1,0,0,1,0,0,1], > [0,1,1,0,1,0,0,0,0,0,1], > [1,0,1,0,0,0,1,0,0,1,0]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,0,1,1,1], > [0,0,0,0,0,1,1,1,0,0,1], > [0,0,0,1,1,0,0,1,0,0,0], > [0,1,1,0,1,0,1,0,0,0,0], > [1,0,1,0,0,0,1,0,0,1,0]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,1,1,1,1], > [0,0,0,0,0,1,1,0,0,1,1], > [0,0,0,1,1,0,1,0,0,0,1], > [0,1,1,0,1,0,0,0,0,0,1], > [1,0,1,0,0,0,0,0,1,0,1]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,1,1,1,1], > [0,0,0,0,0,1,1,0,0,1,1], > [0,0,0,1,1,0,1,0,0,0,1], > [0,1,1,0,1,0,0,0,0,1,1], > [1,0,1,0,0,0,0,0,1,0,1]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,1,1,1,1], > [0,0,0,0,0,1,1,0,0,0,1], > [0,0,0,1,1,0,1,0,0,1,0], > [0,1,1,0,1,0,0,0,1,0,0], > [1,0,1,0,0,0,0,0,0,1,1]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,1,1,1,1,1], > [0,0,0,0,1,1,0,0,0,1,1], > [0,0,0,1,0,1,0,0,1,0,1], > [0,1,1,0,0,0,0,1,0,0,1], > [1,0,1,0,0,0,0,0,1,1,1]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,0,1,1,1], > [0,0,0,0,0,1,1,1,0,0,1], > [0,0,0,1,1,0,0,1,0,0,1], > [0,1,1,0,0,0,0,1,0,0,1], > [1,0,1,0,1,0,1,0,0,1,0]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,1,1,1,1], > [0,0,0,0,0,1,1,0,0,1,1], > [0,0,0,1,1,0,0,0,0,1,1], > [0,1,1,0,0,0,0,0,0,1,1], > [1,0,1,0,1,0,1,0,1,0,1]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,0,1,1,1], > [0,0,0,0,0,1,1,1,0,0,1], > [0,0,0,1,1,0,0,1,0,0,1], > [0,1,1,0,0,0,0,1,0,1,1], > [1,0,1,0,1,0,1,1,0,0,0]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,1,1,1,1], > [0,0,0,0,0,1,1,0,0,1,1], > [0,0,0,1,1,0,0,0,0,1,1], > [0,1,1,0,0,0,0,0,1,0,1], > [1,0,1,0,1,0,1,0,0,0,0]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,1,1,1,1], > [0,0,0,0,0,1,1,0,0,1,1], > [0,0,0,1,1,0,1,0,1,0,1], > [0,1,1,0,0,0,1,0,1,0,1], > [1,0,1,0,1,0,1,0,1,1,0]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,0,1,1,1], > [0,0,0,0,0,1,1,1,0,0,1], > [0,0,0,1,1,0,0,1,0,1,1], > [0,1,1,0,0,0,0,1,0,1,0], > [1,0,1,0,1,0,1,0,0,0,1]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,1,1,1,1], > [0,0,0,0,0,1,1,0,0,0,1], > [0,0,0,1,1,0,0,0,0,1,1], > [0,1,1,0,0,0,0,0,0,1,0], > [1,0,1,0,1,0,1,0,1,0,1]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,1,1,1,1], > [0,0,0,0,0,1,1,0,0,1,1], > [0,0,0,1,1,0,0,0,1,0,1], > [0,1,1,0,0,0,0,0,1,1,0], > [1,0,1,0,1,0,1,0,0,0,1]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,1,1,1,1], > [0,0,0,0,0,1,1,0,0,1,1], > [0,0,0,1,1,0,0,0,1,0,1], > [0,1,1,0,0,0,0,0,1,1,0], > [1,0,1,0,1,0,1,0,0,1,1]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,1,1,1,1], > [0,0,0,0,0,1,1,0,0,1,1], > [0,0,0,1,1,0,1,0,1,0,1], > [0,1,1,0,0,0,1,0,1,1,0], > [1,0,1,0,1,0,0,0,0,1,1]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,1,1,1,1], > [0,0,0,0,1,1,1,0,0,1,1], > [0,0,0,1,0,1,1,0,1,0,1], > [0,1,1,0,0,1,1,0,1,1,0], > [1,0,1,0,0,0,1,0,0,0,1]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,0,1,1,1], > [0,0,0,0,1,1,1,1,0,0,1], > [0,0,1,1,0,0,1,1,0,1,1], > [0,1,0,1,0,1,0,1,0,0,1], > [1,0,0,1,0,1,1,0,0,1,1]])), > BinaryMatroid(Matrix([[0,0,0,0,0,0,0,1,1,1,1], > [0,0,0,0,1,1,1,0,0,1,1], > [0,0,1,1,0,0,1,0,1,0,1], > [0,1,0,1,0,1,0,0,0,0,1], > [1,0,0,1,0,1,1,0,1,1,1]]))] > > -- > > --- > You received this message because you are subscribed to the Google Groups > "sage-matroid" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > For more options, visit https://groups.google.com/d/optout. -- --- You received this message because you are subscribed to the Google Groups "sage-matroid" group. 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