A300985 Number of isomorphism classes of n-elementary gammoids of rank 3.

0, 0, 0, 1, 4, 13, 37, 100, 272, 817, 3007

Offset

0,5

Comments

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.

First differs from A244197 at a(8). - Omar E. Pol, Mar 17 2018

Links

Table of n, a(n) for n=0..10.

I. Albrecht, OEIS_A300985.sage, Sage-8.0 program. The function 'a' computes the sequence.

A. W. Ingleton and M. J. Piff, Gammoids and transversal matroids, Journal of Combinatorial Theory, Series B, 15(1):51-68, 1973.

J. H. Mason, On a class of matroids arising from paths in graphs, Proceedings of the London Mathematical Society, 3(1):55-74, 1972.

Example

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).

Crossrefs

Sequence in context: A048474 A054761 A244197 * A080145 A097551 A224033

Adjacent sequences: A300982 A300983 A300984 * A300986 A300987 A300988

Keyword

nonn,more,hard

Author

Immanuel Albrecht, Mar 17 2018

Status

approved