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Combinatorics and linear algebra of Freiman's isomorphism
Published online by Cambridge University Press: 26 February 2010
Abstract
An original linear algebraic approach to the basic notion of Freiman's isomorphism is developed and used in conjunction with a combinatorial argument to answer two questions, posed by Freiman about 35 years ago.
First, the order of growth is established of t(n), the number of classes isomorphic n-element sets of integers: t(n) = n(2 + σ(1))n. Second, it is proved linear Roth sets (sets of integers free of arithmetic progressions and having Freiman rank 1) exist and, moreover, the number of classes of such cardinality n is amazingly large; in fact, it is “the same as above”: .
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- Research Article
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- Copyright © University College London 2000
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