This chapter discusses several different ways of using some given set of matroids to form a new matroid. The chapter is organized as follows. Section 7.1 looks at three closely related ways of joining two matroids with exactly one common element. Section 7.2 investigates the operations of extension and coextension, which reverse the operations of deletion and contraction, respectively. Section 7.3 uses the techniques of Section 7.2 to examine the relationship between two matroids such that every flat of one is a flat of the other. Finally, Section 7.4 discusses an interesting non-commutative operation for joining two matroids.
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