On linear versions of some addition theorems

Details On linear versions of some addition theorems On linear versions of some addition theorems

2008-02-24

arxiv.org/abs/0802.3523v1

Mathematics

Combinatorics

To appear in Linear and Multilinear Algebra

Scientific paper

Let K \subset L be a field extension. Given K-subspaces A,B of L, we study the subspace spanned by the product set AB = {ab | a \in A, b \in B}. We obtain some lower bounds on the dimension of this subspace and on dim B^n in terms of dim A, dim B and n. This is achieved by establishing linear versions of constructions and results in additive number theory mainly due to Kemperman and Olson.

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