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Journal of the London Mathematical Society 1979 s2-19(2):193-202; doi:10.1112/jlms/s2-19.2.193
© 1979 by London Mathematical Society
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© Oxford University Press

Higher Order Independence in Matroids

Kenneth Baclawski and Neil L. White

Department of Mathematics, Haverford College Haverford, Pennsylvania 19041, U.S.A.
Department of Mathematics, University of Florida Gainesville, Florida 32611, U.S.A.

One may regard vectors in a finite dimensional vector space as being linear forms in a polynomial ring in an obvious way. A collection of linear forms satisfying various linear dependence relations can become independent when each of the forms is raised to the k-th power. In this paper we prove that a certain class of matroids satisfies a "higher order" independence property of this kind. The case k = 2 is of particular importance, and we mention a number of applications to topology, algebraic geometry, electrical networks and chemical kinetics.


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