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Gammoids and transversal matroids. (English) Zbl 0264.05021


MSC:

05C20 Directed graphs (digraphs), tournaments
05B35 Combinatorial aspects of matroids and geometric lattices
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Full Text: DOI

Online Encyclopedia of Integer Sequences:

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

References:

[1] Bondy, J. A.; Welsh, D. J.A, Some results on transversal matroids and constructions for identically self-dual matroids, Quart. J. Math. Oxford, 22, 2, 435-451 (1971) · Zbl 0294.05019
[2] Brualdi, R. A., Induced matroids, (Proc. Amer. Math. Soc., 29 (1971)), 213-221 · Zbl 0219.05061
[3] Brualdi, R. A.; Scrimger, E. B., Exchange systems, matchings, and transversals, J. Combinatorial Theory, 5, 244-257 (1968) · Zbl 0174.29402
[4] Crapo, H. H.; Rota, G.-C, (Combinatorial Geometries (1970), M.I.T. Press: M.I.T. Press Cambridge, Mass)
[5] Ingleton, A. W., A geometrical characterization of transversal independence structures, Bull. London Math. Soc., 3, 47-51 (1971) · Zbl 0222.05027
[6] Mason, J. H., A characterization of transversal independence spaces, (Bruter, C. P., Théorie des Matroïdes (1971), Springer: Springer New York), 86-94 · Zbl 0219.05003
[7] Mason, J. H., On a class of matroids arising from paths in graphs, (Proc. London Math. Soc., 25 (1972)), 55-74, (3) · Zbl 0244.05014
[8] Mirsky, L., (Transversal Theory (1971), Academic Press: Academic Press New York) · Zbl 0282.05001
[9] Perfect, H., Applications of Menger’s graph theorem, J. Math. Anal. Appl., 22, 96-110 (1968) · Zbl 0157.55301
[10] Perfect, H., Independence spaces and combinatorial problems, (Proc. London Math. Soc., 19 (1969)), 17-30, (3) · Zbl 0176.28302
[11] Piff, M. J.; Welsh, D. J.A, On the vector representation of matroids, J. London Math. Soc., 2, 2, 284-288 (1970) · Zbl 0213.29102
[12] Pym, J. S., The linking of sets in graphs, J. London Math. Soc., 44, 542-550 (1969) · Zbl 0167.52204
[13] Welsh, D. J.A, On matroid theorems of Edmonds and Rado, J. London Math. Soc., 2, 2, 251-256 (1970) · Zbl 0214.26301
[14] T. H. Brylawski; T. H. Brylawski · Zbl 0309.05018
[15] T. A. Dowling and D. G. Kelly; T. A. Dowling and D. G. Kelly · Zbl 0297.05026
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