Unformatted text preview: with at most 4 objects of any one kind in each of the following two ways: [Obtain a numerical answer each time.] (a) by the Principle of InclusionExclusion; (b) by constructing an appropriate generating function and evaluating an appropriate coeﬃcient. 4. Construct two nonisomorphic, selfdual, rank 3 matroids on 6 elements; also construct a rank three matroid on 6 elements that is isomorphic to its dual but not self dual. 5. (a) Deﬁne a projective plane, deﬁne Latin square and deﬁne orthogonal Latin squares. (b) State a theorem that relates projective planes and orthogonal Latin squares and sketch its proof. 1...
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 Spring '11
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 Combinatorics, Graph Theory, Vertex, φ, Latin Square, dual graph

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