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Article Dans Une Revue Combinatorica Année : 2014

Plünnecke and Kneser type theorems for dimension estimates

Résumé

Given a division ring K containing the field k in its center and A,B two finite subsets of K\{0}, we give some analogues of Plünnecke and Kneser theorems for the dimension of the k-linear span of the Minkowski product AB in terms of the dimensions of the k-linear spans of A and B. These Plünnecke type estimates are then generalized to the case of associative algebras. We also obtain an analogue in the context of division rings of a theorem by Tao classifying the sets of small doubling in a group.
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Dates et versions

hal-00618241 , version 1 (01-09-2011)
hal-00618241 , version 2 (13-04-2012)
hal-00618241 , version 3 (26-08-2013)

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Cédric Lecouvey. Plünnecke and Kneser type theorems for dimension estimates. Combinatorica, 2014. ⟨hal-00618241v3⟩
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