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Higher Order Independence in Matroids
Author(s) -
Baclawski Kenneth,
White Neil L.
Publication year - 1979
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/s2-19.2.193
Subject(s) - matroid , independence (probability theory) , order (exchange) , mathematics , class (philosophy) , vector space , space (punctuation) , topology (electrical circuits) , algebraic number , polynomial , discrete mathematics , combinatorics , pure mathematics , computer science , mathematical analysis , statistics , finance , artificial intelligence , economics , operating system
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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