A reduction of algebraic representations of matroids
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- by Bernt Lindström PDF
- Proc. Amer. Math. Soc. 100 (1987), 388-389 Request permission
Abstract:
We prove the following result conjectured by M. J. Piff in his thesis (1972). Theorem. Let $M$ be a matroid with an algebraic representation over a field $F(t)$, where $t$ is transcendental over $F$. Then $M$ has an algebraic representation over $F$. The proof depends on Noether’s normalization theorem and the place extension theorem. We obtain the following corollary. Corollary. If a matroid is algebraic over a field $F$, then any minor of $M$ is algebraic over $F$.References
- Serge Lang, Introduction to algebraic geometry, Interscience Publishers, Inc., New York-London, 1958. MR 0100591 M. J. Piff, Some problems in combinatorial theory, Ph.D. thesis, Oxford, 1972.
- D. J. A. Welsh, Matroid theory, L. M. S. Monographs, No. 8, Academic Press [Harcourt Brace Jovanovich, Publishers], London-New York, 1976. MR 0427112
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 100 (1987), 388-389
- MSC: Primary 05B35; Secondary 12F20
- DOI: https://doi.org/10.1090/S0002-9939-1987-0884485-6
- MathSciNet review: 884485