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Solution to a Matroid Problem Posed by D. J. A. Welsh

Published online by Cambridge University Press:  20 November 2018

D. T. Bean
D. T. Bean*
Affiliation:
York University, Toronto
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The pair (S, M) is a matroid if S is a finite set and M a collection of subsets of S such that (1) every subset of a set of M is in M, and (2) all maximal sets in M have a common cardinality. The span of a set A ⊂ S is Γ(A) where y ∈ Γ (A) if and only if y ∈ A or there is A' ⊂ A, A' ∈ M and {y} ∪ A' ∉ M. A maximal set in M is called a base.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 2 , April 1969 , pp. 129 - 131
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Tutte, W., Lectures on matroids. National Bureau of Standards Journal of Research 69B (1965) 1–47.Google Scholar
2. Welsh, D. J. A., On dependence in matroids. Canad. Math. Bull. 10 (1967) 599–603.Google Scholar
3. Edmonds, J., Minimum partition of a matroid into independent subsets. National Bureau of Standards Journal of Research 69B (1965) 67–72.Google Scholar