Premium
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
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom