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A300985
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Number of isomorphism classes of n-elementary gammoids of rank 3.
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1
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0, 0, 0, 1, 4, 13, 37, 100, 272, 817, 3007
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OFFSET
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0,5
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COMMENTS
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A matroid of rank 3 is a gammoid if and only if it is a strict gammoid (Prop.4.8, [IP73]), therefore a(n) is also the number of isomorphism classes of strict gammoids of rank 3.
By duality, a(n) is the number of transversal matroids with n elements and corank 3.
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LINKS
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I. Albrecht, OEIS_A300985.sage, Sage-8.0 program. The function 'a' computes the sequence.
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EXAMPLE
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There are no rank-3 matroids with fewer than 3 elements, so a(0)=a(1)=a(2)=0.
There is exactly one rank-3 matroid with 3 elements, thus a(3)=1.
If n <= 5 then every matroid of rank 3 with n elements is a gammoid.
For n=6 elements, a matroid of rank 3 with n elements is a gammoid, if it is not isomorphic to the polygon matroid of the complete graph on 4 vertices, M(K4).
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CROSSREFS
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KEYWORD
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nonn,more,hard
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AUTHOR
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STATUS
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approved
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