On linear versions of some addition theorems

Shalom Eliahou (1) , Cédric Lecouvey (1)

1 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville

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.

Mots clés: product sets; field extensions; additive number theory; Kemperman; Olson

Domaines: Combinatoire [math.CO]; Théorie des nombres [math.NT]

Shalom Eliahou, Cédric Lecouvey. On linear versions of some addition theorems. 2008. ⟨hal-00258658⟩