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On Matroid Theorems of Edmonds and Rado
Author(s) -
Welsh D. J. A.
Publication year - 1970
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-2.2.251
Subject(s) - matroid , conjecture , welsh , combinatorics , mathematics , partition (number theory) , monotone polygon , discrete mathematics , mathematical economics , philosophy , linguistics , geometry
In this note I show how very general and powerful results about the union and intersection of matroids due to J. Edmonds [19] may be deduced from a matroid generalisation of Hall's theorem by R. Rado [13]. Throughout, S, T, will denote finite sets, |X| will denote the cardinality of the set X and {xt: iel} denotes the set whose distinct elements are the elements x{. A matroid (S, M) is a finite set S together with a family M of subsets of S, called independent sets, which satisfies the following axioms