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Finite Unions of Quasi-Independent Sets

Published online by Cambridge University Press:  20 November 2018

David Grow  and
William C. Whicher
David Grow
Affiliation:
Parks College of Saint Louis University, Cahokia, Illinois 62206
William C. Whicher
Affiliation:
Parks College of Saint Louis University, Cahokia, Illinois 62206
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Abstract

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The analogue of Horn's theorem characterizing finite unions of linearly independent sets in a vector space is shown to fail in the group of integers.

Keywords

43A46
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 4 , 01 December 1984 , pp. 490 - 493
Copyright
Copyright © Canadian Mathematical Society 1984

References

1. Horn, A., A characterization of unions of linearly independent sets, J. London Math. Soc. 30 (1955), 494-496.CrossRefGoogle Scholar
2. Pisier, G., Arithmetic characterizations of Sidon sets, Bull. Amer. Math. Soc. 8 (1983), 87-89.CrossRefGoogle Scholar
3. Rado, R., Axiomatic treatment of rank in infinite sets, Canadian J. of Math. 1 (1949), 337-343.CrossRefGoogle Scholar