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References
Banach, S., Un théoremè sur les transformations biunivoques. Fundamenta Math. 6 (1927), 236–239.
Brualdi, R. A., Symmetrization of R. Rado's theorem on independent representatives. Unpublished paper (1967).
____, An extension of Banach's mapping theorem. Proc. Amer. Math. Soc. 20 (1969), 520–526.
____, A very general theorem on systems of distinct representatives. Trans. Amer. Math. Soc. 140 (1969), 149–160.
____, Comments on bases in dependence structures. Bull. Australian Math. Soc. 1 (1969), 161–167.
____, Admissible maps between dependence spaces. Proc. London Math. Soc. (1970).
____, A general theorem concerning common transversals. To be published in the Proceedings of the Oxford Conference on Combinatorial Mathematics and its Applications, 1969 (Academic Press).
____, On families of finite independence structures. To be published in Proc. London Math. Soc.
Brualdi, R. A. and Scrimger, E. B., Exchange systems, matchings and transversals. J. Combinatorial Theory 5 (1968), 244–257.
Brualdi, R. A. and Mason, J. H., Transversal matroids and Hall's theorem. Submitted for publication.
Dlab, V., The role of the "finite character property" in the theory of dependence. Comm. Math. Univ. Cardinal 6 (1965), 97–104.
Edmonds, J., Matroid partition. Lectures in Applied Mathematics Vol. 1 (Mathematics of the Decision Sciences).
Edmonds, J. and Fulkerson, D. R., Transversal and matroid partition. J. Res. Nat'l. Bur. Standards. 69B (1965), 147–153.
Hall, P., On representatives of subsets. J. London Math. Soc. 10 (1935), 26–30.
Hall, M., Jr., Distinct representatives of subsets. Bull. Amer. Math. Soc. 54 (1948), 922–926.
Hoffman, A. J. and Kuhn, H. W., On systems of distinct representatives. Annals of Math. Studies No. 38, Princeton Univ. Press (1956).
____, Systems of distinct representatives and linear algebra. Amer. Math. Monthly 63 (1956), 455–460.
Ford, L. R. and Fulkerson, D. R., Network flow and systems of representatives. Canad. J. Math. 10 (1958), 78–84.
Mason, J. H., A characterization of transversal spaces. To be published.
Mendelsohn, N. S. and Dulmage, A. L., Some generalizations of the problem of distinct representatives. Canad. J. Math. 10 (1958), 230–241.
Mirsky, L., Transversals of subsets. Quart. J. Math. (Oxford) (2), 17 (1966), 58–60.
Mirsky, L. and Perfect, H., Systems of representatives. J. Math. Anal. and Applics. 15 (1966), 520–568.
____, Applications of the notion of independence to problems of combinatorial analysis. J. Combinatorial Theory 2 (1967), 327–357.
Nash-Williams, C. St. J. A., An application of matroids to graph theory. Proc. Symp. Rome, Dunod (1968), 263–265.
Perfect, H. and Pym, J. S., An extension of Banach's mapping theorem with applications to problems concerning common representatives. Proc. Cambridge Philos. Soc. 62 (1966), 187–192.
Pym, J. S. and Perfect, H., Submodular functions and independence structures. J. Math. Anal. and Applics. 30 (1970), 1–31.
Rado, R., A theorem on independence relations. Quart. J. Math. (Oxford) 13 (1942), 83–89.
____, Axiomatic treatment of rank in infinite sets. Canad. J. Math. 1 (1949), 337–343.
____, Note on the transfinite case of Hall's theorem on representatives. J. London Math. Soc. 42 (1967), 321–324.
Tutte, W. T., Lectures on matroids. J. Res. Nat'l. Bur. Standards 69B (1965), 1–47.
Welsh, D. J. A., On matroid theorems of Edmonds and Rado. J. London Math. Soc. 2 (1970), 251–256.
Whitney, H., On the abstract properties of linear dependence. Amer. J. Math. 57 (1935), 509–533.
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Brualdi, R.A. (1971). Generalized transversal theory. In: Théorie des Matroïdes. Lecture Notes in Mathematics, vol 211. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061072
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DOI: https://doi.org/10.1007/BFb0061072
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