Hyperfinite Transversal Theory

Bosko Zivaljevic

doi:10.2307/2154170

Hyperfinite Transversal Theory

Transactions of the American Mathematical Society ◽

10.2307/2154170 ◽

1992 ◽

Vol 330 (1) ◽

pp. 371

Author(s):

Bosko Zivaljevic

Keyword(s):

Transversal Theory

Download Full-text

A theorem of the transversal theory for matroids of finite character

Discrete Mathematics ◽

10.1016/0012-365x(78)90072-9 ◽

1978 ◽

Vol 23 (1) ◽

pp. 235-240

Author(s):

E Gyori

Keyword(s):

Transversal Theory

Download Full-text

Rado's theorem for polymatroids

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100051677 ◽

1975 ◽

Vol 78 (2) ◽

pp. 263-281 ◽

Cited By ~ 43

Author(s):

Colin J. H. McDiarmid

Keyword(s):

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Rank Function ◽

Fundamental Importance ◽

Matroid Theory ◽

Continuous Analogue ◽

Finite Set ◽

Necessary And Sufficient ◽

Transversal Theory

The theorem of R. Rado (12) to which I refer by the name ‘Rado's theorem for matroids’ gives necessary and sufficient conditions for a family of subsets of a finite set Y to have a transversal independent in a given matroid on Y. This theorem is of fundamental importance in both transversal theory and matroid theory (see, for example, (11)). In (3) J. Edmonds introduced and studied ‘polymatroids’ as a sort of continuous analogue of a matroid. I start this paper with a brief introduction to polymatroids, emphasizing the role of the ‘ground-set rank function’. The main result is an analogue for polymatroids of Rado's theorem for matroids, which I call not unnaturally ‘Rado's theorem for polymatroids’.

Download Full-text