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CONTENTS1. Introduction.............................................................................52. Matroids..................................................................................6 2.1. Notations and basic properties...........................................6 2.2. Gaussian coefficients.......................................................10 2.3. Projective geometries.......................................................11 2.4. Special classes................................................................143....
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The aim of this paper is to study the threshold behavior for the satisfiability property of a random -XOR-CNF formula or equivalently for the consistency of a random Boolean linear system with variables per equation. For we show the existence of a sharp threshold for the satisfiability of a random -XOR-CNF formula, whereas there are smooth thresholds for and .
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