On linear versions of some addition theorems
Combinatorics
2021-08-19 v1 Number Theory
Abstract
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.
Cite
@article{arxiv.0802.3523,
title = {On linear versions of some addition theorems},
author = {Shalom Eliahou and Cédric Lecouvey},
journal= {arXiv preprint arXiv:0802.3523},
year = {2021}
}
Comments
To appear in Linear and Multilinear Algebra